longitudinal wave

Both transverse and longitudinal waves may be represented by sine wave forms. Both types of waves can(a) be reflected,(b) be refracted,(c) interfere,(d) be diffracted.In general, what applies to one set of waves applies equally well to the other. Transverse waves can be polarised whereas longitudinal waves cannot, but this is outside the scope of this book.

inductance of a coil

In 1820, Oersted discovered the magnetic effect of electric current, according to which an electric current produces a magnetic field. The converse effect was discovered and demonstrated by Michael Faraday in UK and by Joseph Henry in USA in the year 1831. They showed that electric current can be produced in a coil of wire with the help of a magnetic field. The phenomenon is known as electromagnetic induction. Many vital devices like generators and transformers work on the principle of electromagnetic induction. The laws of physics governing the phenomenon of electromagnetic induction are known as Faraday's law of electromagnetic induction. The discovery of the phenomenon of electromagnetic induction lent support to the belief of physicists that 'symmetry is beauty in physics'.

congruent figures

Let PQRS be a parallelogram and PR be one of its diagonals. What can you say about triangles PQRC andRSP?Solution:Step 1: In a four-sided figure, opposite sides are congruent. Hence sides Step 2: QR and PS are congruent, and also sides PQ and RS are congruent.Step 3: In a four-sided figure opposite angles are congruent. Step 4: Hence angles PQR and RSP are four side figure.Step 5: Two sides and an included angle of triangle PQR are congruent to two corresponding sides and an included angle in triangle RSP. According to the above postulate the two triangles PQR and RSP are congruent.

1 man 1 cup

Sexes, male and female are distinct in all higher animals including human. Hereditary differences are quite pronounced in male and female individuals.1. Sex of an organism is associated with certain chromosomes, known as sex chromosomes. In human the sex chromosomes are XY in male and XX in female.2. The male which is heterozygous, produces two types of gametes or sperm X and Y. The homozygous female produces only one type of gamete or ovum X.3. An ovum fertilized with Y bearing sperm gives rise to a male offspring (XY) while an ovum fertilized with X bearing sperm produces a female (XX)4. The maleness and femaleness of the offsprings is dependent on the type of sex chromosomes in the zygote.5. The only difference between male and female sex is that the male has a haploid set and the female a diploid set of sex chromosomes.*

biology grade 10

Self Evaluation1. Draw and label the parts of transverse section of monocot root.2. Draw the transverse section of dicot root and label the parts.3. Distinguish the anatomy of dicot roots from monocot roots. Differences between monocot and dicot roots.Monocot rootsDicot roots(0 Xylem is polyarch.(ii) Pith is usually large at the centre.(iii) Metaxylem vessels are generally circular in cross section.(/V) Conjunctive tissue is sclerenchy-matous in monocot roots like maize, (v) There is no secondary growth.Xylem is usually tetrarch. Pith is usually absent. Metaxylem vessels are generally polygonal in cross section. Conjunctive tissue is usually • parenchymatous. Secondary growth is present.Other Important Question4. What are the three tissue systems in the root of a matured plant?The embryo develops into an adult plant with roots, stem and leaves due to the activity of the apical meristem. A mature plant has three kinds of tissue systems — (0 the dermal, (ii) the fundamental and (iii) the vascular system.(/') The dermal system includes the epidermis, which is the primary outer protective covering of the plant body. The periderm is another protective tissue that supplants the epidermis in the roots and stems that undergo secondary growth.(ii) The fundamental tissue system includes tissues that form the ground substance of the plant in which other permanent tissues are found embedded. Parenchyma, collenchyma and sclerenchyma are the main ground tissues.(iii) The vascular system contains the two conducting tissues, the phloem and xylem. In different parts of the plants, the various tissues are distributed in characteristic patterns.

cubic yard calculator

1. Explain the concept of reciprocal lattice. Discuss its properties. What is its importance?2. Derive the Bragg conditions in terms of the reciprocal lattice vectors. (Raj., 1974)3. Explain the concept of Brillouin zones. Give the construction of the first Brillouin zone of an oblique lattice in two dimensions.4. Show that the reciprocal lattice of a simple cubic lattice is another simple cubic lattice. Hence deduce the first Brillouin zone of the simple cubic crystal lattice.5. Show that the reciprocal lattice for a body centred cubic crystal is face centred cubic.(Raj., 1974; Jodhpur, 1968)6. What do you mean by reciprocal lattice? Calculate the reciprocal lattice for a direct fee lattice. What is meant by first Brillouin Zone? (Delhi, 1983)7. Discuss the origin of the geometrical structure factor and the atomic scattering factor in x-ray diffraction and derive suitable mathematical expressions for them. What is the importance of the geometrical structure factor in the analysis of the crystal structures? (Raj., 1977)8. Explain the origin of van der Waals forces in molecular crystal. Show that for van der Waals forces the interaction energy varies as 1 / Rf\ where R is the separation of two interacting atoms.(Raj., 1984)9. Define Cohesive energy and determine its value for crystals of inert gases.10. Obtain the binding energy of an ionic crystal and derive the expression for the Madelung constant. Calculate the value of this constant for a linear ionic lattice. (Raj., 1970)11. Obtain an expression for the total cohesive energy of an ionic crystal in terms of Madelung constant and other parameters.12. State and prove Bloch theorem.13. Discuss the Kronig-Penny model for a linear lattice. How does it lead to formation of energy bands in solid? (Raj., 1983)14. Give Kronig -Penney model of electron in a periodic potential. What are its consequences?(Rohilkand, 1993, 92, 91; Meerut, 1993)

aluminum hydroxide formula

INTRODUCTIONEthers may be considered as the anhydrides of alcohols, as they may be prepared by elimination of one molecule of water from two molecules of any alcohol.e-g-,C2H5OH + HOC2H5—» C2H5OC2H5 + H2OEthyl alcohol (2 mols) Diethyl etherSince alcohols are also alkyl hydroxides, likewise ethers may be called alkyl oxides by analogy to sodium oxide which is also prepared by elimination of the molecule of water from two molecules of sodium hydroxide.Na|OH + H]QNa—» Na —O—Na + H20Sod. hydroxide (2 mols) Sodium oxideR|OH + H|OR—*R — O — R + H20Alkyl hydroxide (2 mols) Alkyl oxideAs the alcohols may be considered as the monoalkyl derivatives of water, so the ethers may be considered as the dialkyl derivatives of water.H—O—H R—O—H R —O —RWater Alcohol EtherEthers also form a homologous series with the general molecular formula C^H^ + 20 where the value of n is always more than one. Ethers possess the general functional group — O — and are in general represented as R — O — R'.

big lots hours

Water power has been used since ancient times by diverting water from natural streams or rivers over various kinds of paddle wheels or turbines. The power output from waterwheels being low people started building high dams from the last century to obtain a substantial head of hydrostatic pressure. Thus, the water under high pressure, flows through the base of the dam and drives turbo-generators producing hydroelectric power. In U.S., about 300 large dams generate 9.5% of its total electrical power production.Although hydroelectric power is basically a non-polluting renewable energy source, it is still associated with serious problems :1. Dams have drowned out beautiful stretch of rivers, wildlife habitat, forests, productive farmlands, and areas of historic, archeological, and geological significance. The construction of big dams have also rendered several farmers and tribals homeless, and without any livelihood.2."The reservoir behind the Aswan High Dam in Egypt has caused the spread of a parasitic worm which caused a debilitating disease. Further, the increase in humidity over a large area because of the reservoir is causing rapid deterioration of ancient monuments and artefacts which were existing over many centuries.3. Since water flow from the dam is regulated as per the requirement of power, dams play havoc downstream because water levels may change from extremes of near flood levels to virtual dryness and back to flood even in a single day. Other ecological factors are also affected because sediments rich in nutrients settle in the reservoir and only small amounts reach the river's mouth.4. Devastating earthquakes, observed near Koyana in India, are attributed to the Koyana dam (Maharashtra) by some Scientists.Many developing countries have great potential for large hydel power projects but due to the above problems, there is lot of opposition from people as well as from Environmental protection organisations.

what is surface area

The surface area of sphere is 4 * `Pi` * r2 square units.Let us see sample problems for the surface area of sphere,Example 1:Find the surface area of the sphere which is of radius equal to 7 cm.solution:Given the radius of the sphere: (r) = 7 cm.we need to find surface area of the sphere.we know surface area of sphere is given by 4 * `Pi` * r2 cubic units.substitute the radius, r = 7 cm in the formula,volume of the sphere = 4 * 3.14 * 72 = 4 * 3.14 * 7 * 7volume of the sphere = 615.44 cm2Example 2:Find radius of sphere which is of surface area equal to 615.44 cm2.solution:Given the surface area of the sphere: 615.44 cm2To find radius of sphere.we know volume of sphere is given by 4*`Pi` * r2 cubic units.equate the given volume of sphere with the formula,volume of the sphere = 4 * 3.14 * r2 615.44 cm2 = 4 * 3.14 * r2 r2 = 615.44 * `(1/4)` * `(1/(3.14)) ` cm2 r2 = 49 r = 7 cm.

electrons and protons

The proton has a mass of approximately 1 a.m.u. and a charge of +e. It is the hydrogen nucleus. The charge is equal and opposite to that on the electron, and its mass is approximately two thousand times as large.When a-particles bombard nitrogen, protons are emitted. Since the proton is smaller than the a-particle it has greater penetrating power. It can be deflected by both magnetic and electric fields, because it is electrically charged.

rounding off numbers

1) 665.3682 becomes:(round to nearest whole number) Solution: In the first step to make a nearest thousand 665.368 The 2 is neglected, because less than 5 Then the second step to rounding the value of 8, it is greater than 5, 665.37 Again in the third step tenth place it is rounded to 4 665.4 And the final result is 665

integration formula

Formulas on Exponential integration1) `int e^(x)dx` = `e^x`2) `int e^(cx)dx` = `(e^(cx))/(c)` 3) `int a^(cx)dx` =`(a^(cx))/(c.ln a)` [ a > 0, a ≠1 ]4) `int_0^oo e^(-ax) sin bx dx` = `b/(a^2 + b^2)` [ a > 0 ] 5) `int_0^oo e^(-ax) cos bx dx` = `a/(a^2 + b^2)` [ a > 0 ]

properties of gases

Groups: A vertical column in the periodic table is termed as a group or family. They are considered to be the most important method of classifying the elements. In some groups, the elements have same properties and show a clear pattern in properties down the group. These groups are to be given trivial names, like the alkali metals, alkaline earth metals, halogens, and noble gases. Some groups in the periodic table show less similarities and these have no trivial names and are simply recognized by their group numbers.Periods: A horizontal row in the periodic table can be defined as a period. Although groups are the common way of classifying elements, there are some regions of the periodic table where the periods are more significant than groups. This can be true in case of d-block or "transition metals", and especially for the f-block, where the lanthanides and actinides form two horizontal series of elements.Blocks: Due to the importance of the outermost shell, blocks can be refered by the different regions of the periodic table, and are named according to the subshell in which the "last" electron is present. The s-block comprises the alkali metals and alkaline earth metals as well as hydrogen and helium. The p-block comprises the groups 13 through 18 and contains all of the semimetals. The d-block comprises groups 3 through 12 and has all of the transition metals. The f-block is comprised of the rare earth metals.Other: The chemical elements are also grouped together in many different ways. Some of these groupings are often stated on the periodic table, like transition metals, poor metals, and metalloids. Other groupings may also be present, which are informal like the platinum group and the noble metals.

energy stored in a capacitor

Q. 51. Find the equivalent capacitance between points A and B in the following diagrams (Fig. 3 • 26).Solution: (i) Capacitors of 8|iFand 8 |xF are in series, then 1112 1— = — + — = — = — => equivalent capacitance q = 4(.iF q 8 8 8 4 Similarly for other branch11-13 + 25 . . t— =--1--=-= — => equivalent capacitance C, = — = 6 uFC2 10 15 30 30 5Now two capacitances Q andC2areinparallel/henceequivalentcnpncitance isC =CX +C2 =4+ 6=10nF (ii) Do yourself like part (i). [Ans. 2(.iF]Q. 52. Three capacitors are connected to a battery of 20 volt as shown in the figure 3 - 27. Calculate:(i) equivalent capacitance of the combination,(ii) charge stored on the capacitor of 3|iF. (1999)Solution : (i) Capacitors of 3(iF and 6 (iF are in series, henceJ__i 1 - 2 + 1Q ~ 3 + 6 ~ 6equivalent capacity C| = = 2 |iFNow capacitors of 2(.iFand 8|.iFare in parallel, hence equivalent capacitance C = 2 + 8 = 10|.iF(ii) Since capacitors of 3|.iFand 6(iFare connected in series with 20 vol t source. Charge on 3|iFcapacitor=charge on series combination of 3 and 6(.iF = Cj x 20 = 2|iFx 20 volt = 40 |iC Q. 53. The combination of four condensers of equal capacity is shown in the fig 3 • 28. If the resultant capacity between the points P and Q is l|iF, find the capacity of each condenser.Solution : Let the capacity of each condenser be C. These condensers are arranged in series in between the points P and Q. Therefore,111114 „ . _- = — + — + — + — = — or C= 4liF1 c c c c cQ. 54. Find the equivalent capacitance between points A and B in the adjoining figure3-29.Solution : Capacitance 2(.iF and 2j.iF are connected in parallel, hence their resultant capacitance Cj = 2 + 2 = 4(iF.Now 8|iF and Cj are in series, theirresultant capacitance^ 8x 4 32 8 _C2 =-= — = —uF8 + 4 12 3Again, 12 (iF and 6|iF are in series, hence their resultant„ 12 x.6 72 . _C, =-= -i— = 4|iF12+6 18» ,ii i „ c,c2Note : — = — + — => C = —C Cj C2 Cx + C2Now C 3 and 4p.F are in parallel, their resultant C4 = C3 + 4|iF = 4^F + 4|iF = 8(iFAgain,C4 and l|iF are in series, their resultant_ C4xl 8x1 8 _Cs = —-=-= - uF' C4+l 8 + 1 9Now C2, the resultant capacitance between C and £ and Cs, the resultant capacitance between C and D are in parallel and their resultant r 8 8 32 .Q. 55. The equivalent capacitance between points A and B in the adjoining figure 3 ■30, is 1 • 0 (iF. Find the capacity of the capacitor C. (1995)Solution : As in last question, it can be shown that capacitance between points P and Q is Q = 2(j.FNow Cj = 2nF is in series with C and their equivalent capacitance is l|iF, hence1=1 I1 ~2 + C1 i 1 1 ' r i n=> —=1--=-/. C = 2 uFC 2 2Q. 56. In the adjoining figure (3 -31) of a circuit, B is earthed and A is kept at 1500 volts. Calculate the potential at point 1Solution: Capacitors of 5 and 5|iFare in series, their equivalent capacitance is 5/2 |iF. Now 5/2 (iF is in parallel with l|iF capacitor, their equivalent capacitance is7/2 (iF. Capacitors of ^and 3-5^= ^j(iFare in series, hence equivalent capacitance isP.D.between/4 and B = 1500- 0=1500 volts7Charge on the combination q=CV Fx 1500 volt = 2625 (iC.-. Charge on capacitor of 3 -5 |.iF = 2625 (.iCPotential difference between A and P= -i_=^C =750 volt. 3-5(iF 3-5nCi.e. 1500 - VP = 750 /.Potential at P, VP = 1500 - 750 = 750 volt.Q. 57. Find the equivalent capacitance between points A and B in the adjoining circuit by drawing its simple equivalent circuit. (2000)Solution : In the given circuit first plate of each capacitor is connected to A and second plate of each is connected to B, hence it is a parallel combination.Equivalent circuit can be drawn as in fig. 3.33Now do yourself. [Ans. 6|xF]Q. 58. Find equivalent capacity between the points A and B in the adjoining diagram (fig.3 -34).Solution : The given circuit consists of two closed mesh, first made of 2,2 and 5|iF and other made of 6,6 and 5nF. This circuit can be rearranged as shown in fig 3-35.According to fig. 3 ■35 given circuit is Wheatstone bridge.2 _ 6 2 6i.e. Ratio of capacitances in sides AC and AD is equal to that of capacitances in sides BC and BD. Hence this is a balanced bridge.There will be no charge on the capacitor of 5|iF. Hence this capacitor can be removed. (Note). Then reduced circuit will be as shown in the fig 3 • 36.Now do yourself. [Ans. 3jiF]Q. 59. Find the energy stored in the capacitor shown in the adjoining figure 3-37. (1995)Solution : Once capacitor is charged „ it will not allow the current to flow.Resistances 2 fl, 3 Q and 5 Q are in series, Their equivalent resistanceR = 2+ 3 + 5= 10 fi This resistance is in parallel with capacitor hence P.D. of capacitorV=iR =2x10 =20 volt /. Energy stored in capacitorU = - CV2 = - x 2 x 10"6 x (20)2 2 2= 4x 10-4 jouleQ. 60. In seady state, find the charges stored and potential difference of two capacitors, shown in adjoining figures-38. (1997,2002)Solution : In steady state, nc current will flow through capacitoi branch, hence equivalent resistance ol circuitR = 4 + 5 + 1= 10 Q ^ 10V .Current i =-= 1 amp.lOfi rv Capacitor branch is in parallel with branch of resistances 4 Q and 5 Q. .•. P.D. of capacitor branchV = ix R' = 1 x (4 + 5) = 9 volt Equivalent capacitanceCj + C2 2+3 Charge stored on capacitor combinationq = CV = 1 • 2nF x 9 volt = 10 • 8 |*C Charge on each capacitor,<h=l2= 10 • 8 |iC P.D. of first capacitor V1=^- = 1C>28^C = 5-4 voltP.D. of second capacitor V2=— =^ ^^ =3-6 voltC2 3nFPotential difference between A and P= -i_=^C =750 volt. 3-5(iF 3-5nCi.e. 1500 - VP = 750 /.Potential at P, VP = 1500 - 750 = 750 volt.

free form amino acids

The following are chemical properties of sulphuric acid:-It is acidic only in water solution when hydronium and sulphate ions are formed. Hydronium ions result in acidic property. It is diabasic as it ionises in two stages- 1 H2SO4 + H2O ↔ H3O+ + HSO4- 2 HSO4- + H2O ↔ H3O+ +SO42-1) It react with metals and form metallic sulphate and hydrogen at ordinary temperature. Mg + H2SO4→ MgSO4 + H22) It neutralises bases to form slats and water. CuO + H2SO4→ CuSO4 + H2O3) It liberates carbondioxide from metallic carbonate (ZnCO3) and bicarbonate(2NaHCO3). ZnCO3 + H2SO4 → ZnSO4 + H2O + CO24)It evolves hydrogen from metal sulphides. F2S + H2SO4 → FeSO45)It evolves sulphurdioxide and sulphites and hydrogen sulphites Na2SO3 + H2SO4→ Na2SO4 + H2O + SO2

science working models

240 volts is the home electricity voltage in India which is supplied to our homes. On voltage of 240 maximum appliances work but some devices like: hair dryer, battery chargers, laptops, radios etc, do not accept 240 volts for them use of voltage converter is must. Three types of voltage converters are there:-Resistors networks TransformersCombination When our appliances are turned on, a force of 240 volts is passed through appliance. The energy is used in completing the works like heating, running motor, lighting, etc it is analogous to the water is forced through the pipe using a mono block pump.

primary resources maths

Ecological efficiency is the percentage of energy transferred from one trophic level to the next. Alternatively, it is the ratio of the net productivity, i.e., the biomasS, at one trophic level to the net productivity (biomass) at the level below. Ecological efficiency varies among organisms. Usually it is 10%. This means that 90% of the energy available at onp trophic level never transfers to the next. (There are number of ratios used to express the efficiency with which organisms exploit their food resources and convert the food into biomass. Important efficiency measures for producers are —1. Photosynthetic efficiency. It is the percentage ratio between gross primary productivity and incident total solar radiation. It generally varies from 1 to 5 per cent.Photosynthetic efficiency_ Gross primary productivity ^ Incident total solar radiation2. Net production efficiency. It is the percentage ratio between net primary productivity and gross primary productivity. It is around 50%.Net production efficiency_ Net primary productivity Gross primary productivityImportant efficiency measures for consumers include —1. Assimilation efficiency. It is the percentage ratio between food energy assimilated and food energy ingested at one trophic level.Assimilation efficiency_ Food energy assimilated ^ ^^ Food energy ingested2. Ecological efficiency. It is the percentage ratio between energy in biomass production at one trophic level and energy in biomass production at previous trophic level. It is also called trophic level efficiency.Ecological efficiency = Energy in biomass production at one trophic level Energy in biomass production at previous trophic level

biology study guide

The data gathered in the experimental study of artificial transmutations are so vast and varied that it is not possible to give here a detailed account of them ; nor can this serve any useful purpose to the general student. It is more profitable to indicate the main guiding principles used in the classification and interpretation of experimental data.

life of pi summary

1. Experiments show that if a discharge tube is exhausted to a low pressure (0.01 mm of Hg), cathode rays are produced.2. Cathode rays are fast moving electrons having a negative charge. They contain the smallest quantity of electricity from nature i.e., 1.602 x 10'19 coulombs.An electron has a mass 9.1 x 10~31 kg and hence is about —— limes lighter 1840than the hydrogen atom.3. Prof. J.J. Thomson proposed the hypothesis that cathode rays were streams ofnegatively charged particles. He was the pioneer who devised an experiment £by which the specific charge — of such particles was determined. m4. Milikan's oil drop experiment was the first direct experimental proof of the atomic nature of electric charge.5. The photoelectric effect is a process whereby electrons can be ejected from a metallic surface when light is incident on that surface. Einstein provided a successful explanation of this effect by extending Planck's quantum hypothesis to the electromagnetic field, in this model, light is viewed as a stream of particles called photons, each with energy E = hv, where v is the frequency and h is Planck's constant The kinetic energy of the ejected photoelectron is given by (hv - wj, where wo is the work function of the metal.6. X-rays from an incident beam are scattered at various angles by elections in a target such as carbon. In such a scattering event, a shift in wavelength is observed for the scattered X-rays, and the phenomenon is known cs the Compton effect. Classical physics does not explain this effect. If the X-rays is treated as a photonconservation of energy and momentum applied to die photon-election collisions yields the following expression for the Comptonshift:-(1-cos a), mcwhere m is the mass of the electron, c is the speed of light and a is the scattering angle.7. All matter exhibits both particle and wave character. The dualistic nature of matter was proposed by de-Broglie. The de-Broglie wavelength of any particle of mass m and velocity v is given by x = t.-±. p mv£and the frequency of matter waves obeys the Einstein relation i) = —, where hE is the total energy of the particle. Subsequent experiments that confirmed the concept of matter waves included the observation of electron diffraction by Davisson and Germer and independently by Thomson.8. The wavelengths of visible objects are far too small for their wavelike nature to be apparent in everyday life. The wavelike nature of electrons becomes visible when they are reflected from single crystals or diffracted by ultra-thin materials.

pa school requirements

Find the co-ordinates of a point which is equidistant from the points (-2,9), (10,-7) and (12,-5) Solution Let the co-ordinates of the required point P be (x,y) which is equidistant from the given points A(-2,9),B(10,-7) and C(12,-5) Now; $PA=\sqrt{(x+2)^{2}+(y-9)^{2}}$ $PB=\sqrt{(x-10)^{2}+(y+7)^{2}}$ $PC=\sqrt{(x-12)^{2}+(y+5)^{2}}$ Since PA=PB $\therefore PA^{2}=PB^{2}$ $\Rightarrow(x+2)^{2}+(y-9)^{2}=(x-10)^{2}+(y+7)^{2}$ $\Rightarrow x^{2}+4x+4+y^{2}-18y+81=x^{2}-20x+100+y^{2}+14y+49$ $\Rightarrow24x-32y=64$ $\Rightarrow3x-4y=8$.......(i) Also, since PA=PC $PA^{2}=PC^{2}$ $\Rightarrow(x+2)^{2}+(y-9)^{2}=(x-12)^{2}+(y+5)^{2}$ $\Rightarrow x^{2}+4x+4+y^{2}-18y+81=x^{2}-24x+144+y^{2}+10y+25$ $\Rightarrow28x-28y=84$ $\Rightarrow x-y=3$....(ii) Solving equation (i) & (ii); x=4;y=1 Hence the co-ordinates of the required point P are (4,1) Ans.

how to make paper look old

ModalsExampleUses 1Can / can'tThey can control their own budgets. We can't fix it. Can I smoke here? Can you help me?Ability / Possibility 1 Inability / Impossibility Asking for permission! Request [Could / couldn'tCould I borrow your dictionary? Could you say it again more slowly? We could try to fix it ourselves. I think we could have another Gulf war. He gave up his old job so he could work for us.Asking for permission! i RequestSuggestion j 1 Future possibility Ability in the pastMayMay I have another cup of coffee?China may become a major economic power.Asking for permission 1 Future possiblity jMightWe'd better phone tomorrow, they might beeating their dinner now.They might give us a 10% discount.Present possibilityI lFuture possibility ,Must / mustn'tWe must say good-bye now.They mustn't disrupt the work more thannecessary.Necessity / Obligation / ProhibitionOught toWe ought to employ a professional writer.Saying what's right or correctShallShall I help you with your luggage? Shall we meet at 2.30 then? Shall I do that or will you?OfferSuggestion Asking what to doShouldWe should sort out this problem at once.I think we should check everything again. Profits should increase next year.Saying what's right or correctRecommending action Uncertain predictionWiU / won'tI can't see any taxis so I'll walk. I'll buy it for you if you like. I'll get back to you on Monday. Profits will increase next year.Instant decisionsOfferPromiseCertain predictionWould / wouldn'tWould you mind if I brought a colleague with me?Would you pass the salt please? Would you mind waiting a moment? "Would three o'clock suit you?" - "That'd be fine."Would you like to play golf this Friday? "Would you prefer tea or coffee?" - "I'd like tea, please."Asking for permissionRequest RequestMaking arrangementsInvitation Preferences

sine cosine tangent chart

The sine term and cosine term is a ratio of sides in the right angled triangles is called tangent tables. The three relations as follow First, tan A = `(sin A)/ (cos A)` Second, assume sin A = `p/r`. Third, cos A = `q/r` Dividing `p/r` by `q/r` and canceling the r's that appear, we conclude that tan A = `p/q`. That the tangent is the opposite side divided by an adjacent side: Tan A = `(opp)/(adj)`How to find Tan values of angles in radiansAny radian angle can be converted to degree and vise versa.Î radian = 180 degreesWe know the value of Î is 3.14 approximatelySo 1 radian = 180 degree / 3.14 = 52.325 degreesNow we can find any radian measure with this conversion factor in hand. A Tangent tables by using sine term and cosine term The two triangles PST and PQR are similar, we have `(TS)/(PT) = (RQ) / (PR)`.But Here TS = tan A,PT= 1, RQ = sin A, and PR = cos PQ. Therefore we have derived the fundamental identity Tan A = `( sin A) / (cos A)`

half life equation

1. Find the values of the disintegration constant and half-life of a radioactive substance for which the following counting rates were obtained at different times.What would have been the counting rate at t = 0?2. The counting rates listed below were obtained when the activity of a certain radioactive sample was measured at different times. Plot the decay curve on semilog paper and determine the half-lives and initial activities of the component activities.

periodic table picture

Help on learning table of Pythagorean related trigonometric identities:cos2θ + sin2θ = 1sin θ = ± `sqrt(1 - cos^2 theta)`cos θ = ± `sqrt(1 - sin^2 theta)`sin θ = `1/(csc theta)`cos θ = `1/(sec theta)` tan θ = `1/(cot theta)`csc θ = `1/(sin theta)` sec θ = `1/(cos theta)` cot θ = `1/(tan theta)`1 + tan2θ = sec2θ1 + cot2θ = csc2θsin θ = ± `(tan theta)/(sqrt(1 + tan^2theta))`cos θ = ± `1/(sqrt(1 + tan^2theta))`tan θ = ± `sqrt(sec^2 theta - 1)`csc θ = ± `(sqrt(1 + tan^2theta))/(tan theta)` sec θ = ± `(sqrt(1 + tan^2theta))`cot θ = ± `1/(sqrt(sec^2 theta - 1))`Help on learning table of symmetry related trigonometric identities:sin (-θ) = - sin θ cos (-θ) = + cos θ tan (-θ) = - tan θ csc (-θ) = - csc θ sec (-θ) = + sec θ cot (-θ) = - cot θ sin (� - θ) = + sin θcos (� - θ) = - cos θtan (� - θ) = - tan θcsc (� - θ) = + csc θsec (� - θ) = - sec θcot (� - θ) = - cot sin (`pi/2` - θ) = + cos θcos (`pi/2` - θ) = + sin θtan (`pi/2` - θ) = + cot θcsc (`pi/2` - θ) = + sec θsec (`pi/2` - θ) = + csc θcot (`pi/2` - θ) = + tan θHelp on learning table of shifts and periodicity related trigonometric identitiessin (θ + `pi/2` ) = + cos θ cos (θ + `pi/2` ) = - sin θ tan (θ + `pi/2` ) = - cot θ csc (θ + `pi/2` ) = + sec θsec (θ + `pi/2` ) = - csc θ cot (θ + `pi/2` ) = - tan θ sin (θ + �) = - sin θcos (θ + �) = - cos θtan (θ + �) = + tan θcsc (θ + �) = - csc θsec (θ + �) = - sec θcot (θ + �) = + cot θsin (θ + 2�) = + cos θcos (θ + 2�) = + sin θtan (θ + 2�) = + cot θcsc (θ + 2�) = + sec θsec (θ + 2�) = + csc θcot (θ + 2�) = + tan θ

the area of a triangle

Some notes for area of triangle in circle: If the circle contain a triangle inside, we can easily calculate the area of triangle. The area of triangle is based on length of sides. We can find the area of triangle in circle is same as normal triangle area calculation.Formula for area of triangle in circle in math: For finding the area of the equilateral triangle use the simple form as A = ½ bh.The base length and height is more important for area of triangle in circle calculation. In circle, the triangle has different length of sides means we can use the heron’s formula. The perimeter is divided as half. This part is called as semi perimeter. The area of triangle in circle is = `sqrt(s (s-a) (s-b) (s-c))` . where s is represent the semi perimeter as s = `(a + b + c)/2` . If the triangle has angle size in circle means use the trigonometry formula as Area = `1/2` ab.sin c. Here two side’s length are used.

solute definition

Example problem 1 to define exponential function help:Solve the exponential function, f ( x ) = x54 x7Solution:The given function is f (x) = x54 x7The given function is of the form`e^a. e^b = e^(a+b)`Therefore we can solve the given function by using the formula f (x) = x54 x7 = x 54 + 7So we get, f (x) = x61Therefore the solution for the given function will be f (x) = x54 x7 = x61Example problem 2 to define exponential function help:Solve the exponential function, y = f (x), where y = `e^54/e^7`Solution:The given function is f (x) = `e^54/e^7`The given function is of the form`(e^a) / (e^b) = e^(a - b)` Therefore we can solve the given function by using the formula f (x) = e54 - 7So we get, f (x) = e47 Therefore the solution for the given function will bef (x) = `e^54/e^7` = e47.

point of concurrency

In line design geometry section we have many types of lines which has property of its own.Lines are classified into following types. Parallel lines: In geometry parallel lines are mostly applicable in design section, two lines which does not touch each other are called parallel lines.Perpendicular lines: In geometry Perpendicular lines are mostly applicable drawing section,Two line segment that form a L shape are called perpendicular lines.Concurrent lines: The three or more lines passing through the same point are called concurrent lines.

math 216

Maths problem 1:Find the midpoint between given two points A (21, 49) , B (6, 23)In co-ordinate geometry, the midpoint formula between the two points (x1, y1) and (x2, y2) is (`(x_1 + x_2) / 2,``(y_1 + y_2) / 2` ). Given points are A (21, 49) , B (6, 23)(x1, y1) is A (21, 49) (x2, y2) is B (6, 23) Midpoint between the two points = (`(x_1 + x_2) / 2` , `(y_1 + y_2) / 2` ) = (`(21+6) /2` , `(49+ 23) / 2` ) = (`27/ 2` , `72/2` ) = (13.5, 36) Midpoint between the two points A (21, 49) , B (6, 23) = (13.5, 36) Maths problem 2:Solve the given problem 20(s –11) – 10s - 18 = 20(s + 32)The Solutions follows below:Given expression is,20(s –11) – 10s `- ` 18 = 20(s + 32)Multiplying the integer terms20s – 220– 10s – 18 = 20s + 640.Grouping the above terms10s –-238= 20s + 640Add 238on both sides10s –-238+ 238 = 20s + 640 + 238Grouping the above terms10s = 20s + 878Subtract 20s by on both sides10s `-` 20s = 20s `-` 20s +878Grouping the above terms–10s = 878S = `- 878/10`The required answers is S = `- 878/10`

formula volume

The following formulas are used to measure the volume of some basic solid shapes.The volume of a cube = a3The base unit for volume of cube is cubic unitsThe volume of a cylinder = `pi r^2 h`The base unit for volume of cylinder is cubic unitsThe volume of a cone = `1/3 pi r^2 h`The base unit for volume of cone is cubic unitsThe volume of a sphere = `4/3 pi r^3`The base unit for volume of sphere is cubic units

whole number definition

Introduction of algebra whole numbers: The meanings of an algebra whole numbers, and commonly-used fractions and decimals (for example 3/4, 0.75) and representing the equivalent forms of the same number through physical models, drawings, calculators, and computers;

declarative sentence

82. Study the-following examples :—Noun ClauseComplex. He said that he yvas innocent.*Simple. He declared his innocence;■Complex. That you are drunk aggravates your offence.Simple. - Your drunkenness aggravates your offence.Complex. , Tell me where you live-Simple. Tell me your address.Complex. It is a pity that we should have to undergo this disgracedSimple. Our having to undergo this disgrace' is a pity.Complex. It is proclaimed that all men found with arms will be shotSimple. According to the proclamation all men found with arms will tie shotComplex. He remarked how impudent the boy was.Simple., He remarked on the boy's impudence. Complex. How long I shall stayAs doubtful.Simple. The duration of my stay is doubtful. ■Complex. Except that, heliurt his hand,, he was lucky;Simple. * Except for the hurt to his handy he was lucky.Exercise 79. Convert each, of the following Complex sentences to a Simple sentence:1. We believe that he is innocent2. It was much regretted that.he was absent,3. The consequence of, his carelessness was that the game was lost.4. He asked why Icame.,5. He ordered that the traitor should be executed,6. It is to be hoped that he escaped unhurt.* 7. T do not know when X shall return.8. We hope that better times will come.9. The news that the enemy landed spread like wild fire,,10. That I was successful does not make me happy.,1,1. He ordered the. police that they should imprison, the rioters.12. That you should be willing to believe this is incredible,13. Whoever, is prudent is respected, '14. It is reported that our troops have won a victory.15. All believed that he was guilty of murder. -16. Tell me what you mean, by this,83. Study the following examples:—

saxon math answers

Introduction for ' answers me ':Through online, the students can get math answers for their problems at any time. There are number of math websites available for the students to get math answers. Students can learn math from their home itself.In this article answers me , we are going to discuss some math problems which are provided with answers.

atomic number definition

These experimental observations enabled Rutherford and Soddy to formulate a theory of radioactive change. They suggested that the atoms of radioactive elements undergo spontaneous disintegration with "the emission of a- or /3-particles and the formation of atoms of a new element. Then the intensity of the radioactivity, which has been called the activity, is proportional to the number of atoms which disintegrate per unit time. The activity, A, measured by one of the methods discussed in Chapter 2, may then be replaced by the number of atoms N, and Eq. (10-1) may be writtenis the equation which represents the change with time of the number of atoms of a single decaying radioactive substance. Differentiation of both sides of Eq. (10-4) giveswhere N(t) has been abbreviated as N. According to Eq. (10-5), the decrease "per linit time in the number of atoms of a radioactive element because of disintegration is proportional to the number of atoms which have not yet disintegrated. The proportionality factor is the disintegration constant, which is characteristic of a particular radioactive species.Equation (10-5) is the fundamental equation of radioactive decay. With this equation, and with two assumptions, it was possible to account for the growth of activity in the thorium or uranium fractions from which the ThX or UX had been removed. The assumptions are (1) that there is a constant production of a new radioactive substance (say UX) by the radioactive element (uranium), and (2) that the new substance (UX) itself disintegrates according to the law of Eq. (10-5). Suppose t^at Q atoms of UX are produced per second by a given mass of uranium, and let N be the number of atoms of UX present at time t after the complete removal of the initial amount of UX. Then the net rate of increase of UX atoms in the uranium fraction isEquation (10-7) is the same as the recovery equation (10-2) so that the theory gives the correct result for the growth of activity in the uranium or thorium after the removal of the X body. Equation (10-7) also shows that the number of UX atoms in the mass of uranium approaches an equilibrium value for large values of t given by -the ratio

female reproductive formula

Introduction to human egg fertilizationMammals show sexual reproduction. Sexual reproduction involves the fusion of gametes, or sex cells. Female sex cells called egg cells or ova, fuse with the male gametes, called spermatozoa or sperm. The resulting cell, the zygote develops into a new individual. In sexual reproduction the genetic material of the two individuals are mixed and combined to produce an individual that is genetically different from either parent.

types of asexual reproduction

The Penicillium reproduce, asexually by conidia. The conidiophores arise from aerial hypha as well as from those that are submerged in the substratum. These are simple with generally smooth walls or sometimes, the walls may become roughened due to granulations, echinulations or even warts. The conidiophores may either be single or may form clusters or fascicles. These may be of one of the following two distinct types.

amino acids classification

Pesticides are chemicals, which are used to kill unwanted insects, fungus, rodents etc. They areRodenticides (Kill rodents and some other mammals)Fungicides -- . Pesticides ->-' Herbicides (Kill plants)(Kill fungi ana plantbacterial pathogen) -IInsecticides (Kill insects)important component for high input farming and, therefore, there is a strong tendency at presentto resort to the use of pesticides.The term pesticide is a broad one. Classification of pesticides is shown below in Table 10.7.PesticidesDefinitionExamples :InsecticidesA substance or mixture of substances usedfor killing unwanted insects.Benzene hexachloride, DDT, parathion,diazinon, metathion, methiocarb, aldrin,p-dichlorobenzene.HerbicidesThe chemicals, which are used inagricultural fields to control or kill theherbs, weeds and bushes.2, 4 - dichlorophenoxy acetic acid,2, 4 - dichlorophenol,sodium trichloroacetateFungicidesFungicides are those chemicals which whenapplied to the plants or to their seeds,inhibit or prevent fungi, parasitic plantscomprising the molds, smuts, mildews,rust, etc.Dithocarbamates, bordeaux mixture.

line equation

Introduction to writing equations of parallel lines:

basic online calculator

1. It will decrease due to decrease in collector current.A /r2. IS - A/ . M, ('.A/., 120 x 100 x 10 Aâ– 12 * 10 3 A3. Reverse biasing.4. (0 for rt-type . arsenic. (/'/') forp-typc. IndiumTruth TableABY - A + B0010101001107. (a) Diode is reverse biased because /?-type of thediode is at lower potential. (.b) Diode is reverse biased because p-typc of the diode is at lower potential.(c) Diode is forward biased because p-type of the diode is at higher potential.(d) Diode is forward biased because p-type of the diode is at higher potential.8. In n-type semiconductor charge carriers are electrons and mobility of electrons is more than that of holes.9. 1. Band gap 2. Biasing 10.16. It's more than one.17. p-type18. Energy gap decreases.19. Width decreases.20. Width of depletion region increases.21. Solar cell is a device for converting solar energy into electricity. It is basically a.p-n junction operating in a photovoltaic mode. When light photons fall at the junction, electron-hole pairs are generated. These move in opposite directions due to junction field. These charges accumulate at the two sides of the junction and photo-voltage is developed. It is used in calculators etc.

virtualization definition

Ten Steps to Doing Math study guide notes HomeworkAnalysis related textbook material.Analysis appropriate lecture notes.Entire homework carefully complete.Mark all problem steps.Value reasons for problem steps.For hard problems repeat 1 -5 and analysis like problems, call another student, use other references, and see a tutor or teacher.Conclude by working a problem successfully.Remember main concepts.Formulate note cards for difficult concepts.Do not get behind.Ten Steps to Doing Online math study guide notes HomeworkAnalysis related textbook material.Analysis appropriate lecture notes.Perform homework efficiently.Mark all problem steps.Realize basis for problem steps in its place of using the click and go method.For difficult problems use the resources provided by the software (videos /tutor line).Finish by working a problem successfully.Remember important concepts.Develop virtual note cards by using www.tutorvista.comDon’t get behind you could get block out.

molar mass of oxygen

Introduction to metric measurement mass: The mass or the weight of the objects is a measure equal to the force exerted by the gravitational force on the same object. There are the measurements like the S.I unit, metric unit and other conventional units of mass measurement. The metric unit is based on the base unit the gram. In this article we will see about the metric unit of the mass measurement.

rounding rules

Notation of Integers:The general form of integers isZ= {……-2,-1, 0, 1, 2…}The Basic operations in math areAdditionSubtractionMultiplicationDivisionThe main rules that are used in the place of basic arithmetic operations:Estimation: Estimation means generally rounding to the nearest value. For Example 99 is rounded to the value 100. Because 99 is very nearer to 100. The values 91,92,93,94 are rounded to the value 90 because these are less than 95. The values 95,96,97,98 and 99 are rounded to the value 100 because it is greater than or equal to 95.

2d shapes

DeviationA ray of light of a single colour incident on an equilateral glass prism is refracted towards the normal N| and travels through the glass at reduced speed. When it emerges into the air it is refracted away from the normal N2 and speeds up again. The ray has been deviated from its original direction; the angle of deviation D is the angle between the original and final directions, as shown in Fig. 17.1. The three prisms in Fig. 17.2(a) have been placed so that they 'deviate' three parallel rays to a single point F. A converging (convex) lens can be thought to consist of a set of differently shaped prisms. In Fig. 17.2(b) rays of light from a point O are deviated by the different sections of the lens to form a real image at 1. This is covered in greater detail in Chapter 18, p.221.

elasticity formula

One Mark Questions With Answers1. What is a rigid body ?A body which experiences a small deformation when a sufficiently large force is applied is considered to be rigid.2. When is a body said to be perfectly elastic ?A body is said to be perfectly elastic if it tends to resist deformation. It recovers completely from the deformation once the deforming force is removed.3. When is a body said to be perfectly plastic ?If a body does not recover its original state when the external force is removed but retains its altered state, it is said to be perfectly plastic.4. Define stress.When an external force F is applied uniformly over a surface of area A then the force per unit area is called stress. (Stress = F/A)5. Define strain.The fractional change in the dimension of a body produced by the external force acting on itis known as strain.6. What is the SL unit of stress ?SI unit of stress is Nm~2.7. What is the dimensional formula for stress ?[stress] = [M'L-'r2]8. What is the SI unit of strain ?Strain has no unit.9. State Hooke's law.The law states that, provided the strain is small stress is directly proportional to strain.10. Define coefficient of elasticity.It is the ratio of stress to strain.11. Define Young's modulus.It is the ratio of stress to longitudinal strain.12. What is the SI unit of Young's modulus ?SI unit of Young's modulus is Nm~2.13. What is the dimensional formula for Young's modulus.[Young's modulus] = [M1 L_1T~2]14. Define Rigidity modulus.Rigidity modulus is defined as the ratio of tangential stress to shearing strain.15. What is the SI unit of* Rigidity modulus ?SI unit of rigidity modulus is Nnr2.16. Define Bulk modulus.It is the ratio of stress to volume strain.17. What is the SI unit of bulk modulus.SI unit of bulk modulus is Mm"2.18. What is the dimensional formula of Bulk modulus.[Bulk modulus] = [MW2] Two Marks Questions1. What is elasticity ?2. Distinguish between elastic and plastic materials.3. State and explain Hooke's law.4. Define stress and strain.5. Explain why a rubber tube is longer when suspended vertically than when placed horizontally on a table.6. If the stress to which a wire is subjected is equal to the Young's modulus of its material, find the relation between the initial and final lengths of the wire.Five Marks Questions1. State and explain Hooke's law. Explain the terms elastic limit, yield point and breaking stress.2. Define the three moduli of elasticity. What is the SI unit of the modulus of elasticity ?3. Explain the terms stress and strain.

discovery of oxygen

Q. 8. How Thomson discovered 'isotopes' from the analysis of positive rays ? How did it clear the anomaly of fractional atomic masses? (1996, 98)Or How are the isotopes discovered with the help of analysis of the properties of positive rays? (2001,02)Ans. Isotopes : The atoms having different masses but possessing same atomic numbers (or same chemical properties) are called isotopes.Discovery of Isotopes : When Thomson was studying the mass spectrograph of neon gas, he found two parabolas. He explained this fact by saying that the neon gas contains two kinds of atoms which can not be separated chemically, meaning that, they possess same chemical properties or same atomic number but thier ions have different values of e/M. That means they have different masses. For the first time he used the word 'isotopes' for these atoms having same atomic number but different masses. In this way, the study of positive rays lead to the discovery of isotopes.Thomson also measured the intensities of two parabolas and stated that, the two isotopes of neon having atomic masses 20 and 22 are present in the neon in the ratio of 9:1. Therefore, average atomic mass of neon is given by9x20 + 1x22 =2Qi 2 9 + 1Thus discovery of isotopes in neon also cleared the anomaly of fractional atomic mass of neon. Later on Aston confirmed the existence of isotopes in chlorine also.

define pitch

The following are associated with musical notes: A amplitude B intensity C pitchD timbre (quality) E speed.Which of the above Q1 is determinedby the fundamental frequency of the note?Q2 is determined by the presence of overtones? Q3 is constant for all sounds produced by an orchestra? Q4 can be used to distinguish between different musical instruments? (L). Questions 5-8The diagrams which follow show the waveforms of five musical notes displayed successively on a cathode ray oscilloscope without adjusting its controls.Which waveform shows Q5 the note with the greatest number of overtones? Q6 the note of largest amplitude? Q7 the note with the highest pitch? Q8 the note with the lowest frequency? (L)Q9 (a) Define the terms wavelength, frequency and velocity as applied to. a wave. State a relalionship between them.(b) Describe, in detail, an experiment you would carry out to measure the speed of sound in air. Explain how the result would be calculated from your measurements,(c) State two differences between an electromagnetic wave and a sound wave, both of wavelength 1 metre.(d)Name two types of electromagnetic wave with wavelengths less than 1 metre. (C)Q10 Which one of the following is not an example of a transverse wave? A a sound wave B a light waveC a wave on the surface of the bathwater D a wave on a skipping rope which is shaken E a ripple in a flag on a windy day (NEA)Qll A man sees 'steam' start to come from a factory whistle and 3 seconds later he hears the sound. The velocity of sound in air is 360 m s"1. The distance from the'man to the whistle (in metre) isA 120. B 780. C 960. D 1080 E 2160. Q12 A sonar signal (a high frequency sound wave) sent vertically downwards from a J hip is reflected from the ocean floor and detected by a microphone on the keel 0.4 s after transmission. If speed of sound in water is 1500 ms-1, what is the depth, in m, of the ocean? A 150 B 300 C 600 D 3000 E 6000 (AEB) Q13 (a) Explain the meaning of the terms amplitude and frequency <A a vibration.Describe the effect of changing these two quantifies with respect to(i) the light emitted by a lamp,(ii) the sound emitted by a source of sound.The diagram shows a vibrating tuning fork. The timeitaken for a prong to go from A to B Is s.ouuWhat is the frequency of the vibration? If the velocity of sound in air is 330 m s"1 what is the wavelength of the note emitted by the fork? (AEB}Q14 Explain the difference between longitudinal and transverse waves. Give one example of each kind of wave.Explain how waves transfer energy from one place to another.Ripples are sent across a pond and a small floating object goes up and down six times in 15 seconds. If the wave crests are 40 cm apart, calculate the speed of the waves across the pond. (WjQ15 State three similarities and three differences between the water waves on a ripple tank and sound waves in air.A set of plane waves on a ripple tank reaches a portion of the tank where the water is shallower. The boundary of _ the shallow water is at an angle of approximately 45 ° to the wave fronts. Explain, with the aid of a diagram, what happens to the waves as they enter the area of shallow water.Name two types of electromagnetic waves and explain three ways in which they differ from each other. (JMB) Q16 Describe how you would find the speed with which sound travels in air, by experiment,A radio station broadcasts on a frequency of 200 000 Hz and the wavelength of its signal is 1500 m. Calculate(a) the speed of radio waves in m s"1,(b) the wavelength of the signal of another station that broadcasts on a frequency of 1250 000 Hz.State, and explain, two differences between sound waves and light waves. (C)Q17 (a) A flexible metal strip presses lightly against the teeth of a cog wheel as it rotates uniformly at 600 revolutions per minute. If the wheel has 50 teeth find (i) the frequency, and (ii) the wavelength of the note which it emits in air, given that the speed of sound in air is 340 m s"1.If the wheel is now rotated at 300 revolutions per minute, explain whether the time taken for the sound to reach a distant observer will be charged.What will be the effect, if any, on the pitch of the note emitted if the temperature of the surrounding air now increases by several degrees, all other factors remaining unchanged? Explain your answer, (b) Explain the meaning of (i) echo, and (ii) resonance. Describe in detail how one of these two phenomena can be used to determine the speed of sound in air. (L) Q18 A wheel has 50 spokes and rotates at 10 revolutions per second. Calculate the frequency of the note obtained by holding a card lightly against the spokes as they rotate. What would you expect to observe if a source of sound of frequency 502 Hz was placed near the card?Describe briefly how you would use a stroboscope to check the rate of rotation of the wheel. (S)

binary number converter

26. What is an ideal gas ?A gas which obeys Boyle's law and Charle's law at all temperatures and pressures is called an ideal gas or a perfect gas.27. Write down the perfect gas equation.PV = RT for 1 mole of a gasPV = nRT for n moles of a gas where R is the universal gas constant.28. Give the SI unit of R. It is J moP1 K"1.29. Why gas laws are generally expressed with reference to absolute scale of temperature ?This is because of simplicity in their mathematical forms.30. Give the relation connecting gas constant(/?), Avogadro's number (A^) and the Boltzmann constant (fc)R = KNa)31. A sample of an ideal gas occupies a volume V at a pressure P and absolute temperature 7*. The mass of each molecule is m. If k be the Boltzmann constant then what is the expression for the density p of the gas ?32. Give the dimensional formula of gas constant R.[R] = [ML2T"V2]33. What is an isothermal process ?An isothermal process is origin which the changes in pressure and volume of a given mass of gas take place at constant temperature.34. Which gas law holds good for an isothermal change ? Boyle's law35. What is an adiabatic process ?An adiabatic process is one in which the changes in volume and pressure of a given mass of gas take place such that heat is neither allowed to enter nor leave the gas.36. Will temperature remain constant in an adiabatic change ? \ No. Temperature of the gas undergoes a change. \37. Give an equation which represents an adiabatic change. \ PVy = constant where y = C /C . ■' \' p V \38. What is an isothermal ?A graph of pressure (P) versus Volume (V) for an isothermal process is called an isothermal.39. What is an adiabatic curve ?A graph of pressure (P) versus Volume (V) for an adiabatic process is called an adiabatic curve.40. Isothermals at two different temperatures Tl and T2 of an ideal gas are as shown in the figure. What is the relation between Ty and T2 ?T > T2 V(v Temperature of the isothermal farthest from the origin will be maximum.)41. If an isothermal and an adiabatic curve are drawn on the same scale for the same initial state of a gas, which curve will have a greater slope ?The adiabatic curve is steeper than the isothermal curve. That is, adiabatic curve will have a greater slope.42. Write the equation of state for an ideal gas. PV = nRT for n mole of an ideal gas.43. Write Vander Waal's equation of state applicable for a real gas.P +-^r\(V-b) = nRT where a and b are constants.I V2 J44. What is the effect on the pressure of a gas if it is compressed at constant temperature ?The pressure of the gas increases according to Boyle's law.45. A gas contained in a sealed container is heated up. What is the effect on pressure ? The pressure of the gas increases according to Charle's law.46. When an automobile travels for a long distance the air pressure in the tyres increases. Give reasons.When an automobile travels along a road work is done against the frictional force between the tyres and the surface of the road. The work done is converted into heat which rises the temperature of air inside. Hence air pressure in the tyres increases.47. What is the value of molar gas constant R 1 R = 8.315 J mor'K-*.48. What is the physical significance of molar gas constant R ?It represents the work done or energy supplied in increasing the temperature of 1 mole of a gas through 1 K.49. What happens when a gas is compressed adiabatically ?In the adiabatic compression of a gas, volume decreases while pressure and temperature increase.50. What is the ratio of slope of an adiabatic curve to the slope of an isothermal curve ?Slope of isothermal curve = m, = P Slope of adiabatic curve - m2 = yP•'• m2/mi=Y Two Mark Questions1. Define volume co-efficient and pressure co-efficient of a gas.2. State and explain Boyle's law.3. State and explain Charle's law.4. Explain Kelvin scale of temperature on the basis of Charle's law.5. Why real gases deviate from ideal gases ?6. Evaluate molar gas constant R using perfect gas equation ?7. Give any two characteristics of an isothermal change.8. Give any two characteristics of an adiabatic change.9. Obtain the dimensional formula of R.10. Explain briefly Vander Waal's equation of state. Five Marks Questions1. Explain the two co-efficients of expansion of a gas.2. State Boyle's law and Charle's law. Deduce the perfect gas equation.3. Explain Charle's law and Gay Lussac's law.4. Distinguish between isothermal and adiabatic changes.

integration by parts examples

All problems given as worked examples and exercises are designed to test the understanding, application and computation skills of the students. However, the following problems are included from the point of view of a student who appears for competitive examinations like IIT, etc.

specific heat water

The standard enthalpy of formation or heat of formation of a compound is the enthalpy change accompanying the formation of one mole of a compound from its elements, all substances being in their standard states. It is denoted by ΔHof. The standard state of any substance is taken as in its natural state at 25oC under one atmospheric pressure.