Page 1 : Oueriew, , shinee EAN Sh EEL EA ALLLE AAA LEELALLOLILOLL LIDIA:, , , , 12. Average, RMS and most probable Speed, , 13. Degrees of freedom, , 14. Law of equipartition of energy, , 15. Specific heat capacities of gases, , 16. Specific heat capacity of solids ( Dulong and Petit, 17. Variation of specific heat of solids with temperatur, , 18. Specific heat of water, , 19. Mean free path, 20. Avogadro Number, 21. Brownian motion, , ta, Reese, Seer, eee, Recah, oe, pees, oi., Baie, x, Bec:, nf, y, 3, 4, 'g, ;, ye, i, b, Be, iy, r, Bi, oh, p, b, Bi., Ee, DS, | th, gq, P, p, , , , Clark Maxwell (1831 — 1879), Boltzmann (1844 - IX, and Willard Gibbs (1839 — 1903) completed the kinetic then f, , , , GAS LAWS (IDEAL GAS LAWS), , We shall now derive the relations between pressure", volume (V) and temperature (T) for an ideal gas which °F, established over years through observations and expermne®, laws are called gas laws., , , , , , ( nile, [he relationship between any two physic ‘al on a, v VD) used to specify the state ya go beeps eS, , , , > - 77 ; |, 1002. f eording lo this law the v volume Of a given —, , | Lag | is pa lied, , if T = Constant, , : Apnerseests?

Page 2 : P, Pye 5, , , , , , , , , , , , , , , , , law re, , , , , , gs (ii) temperature of gas and (tii) the, , : V, be the initial pressure and y, 4 \s the final pressure and volume, , = constant, , PV,, ©, Fig. 1, , / his law was discovered by Alexander, , absolute temperature., , (Et eee, mm, , Constant, , rPV« Constant, , (1), Pends on (i), , Units in Which, , Olume of, , the as, , at Constant, , Higher, temperature, , , , , , , , , , , , e and temperature of, , volume of given mass of gas, , ~. of its volume at 0°C for, , , , , , , , if temperature ig 2°C, V. = Vo [ + a, , ; 273-15, “ Volume of gas at c, , , , YN (i+) a 27315 +t, 273.15 ) = Yo 273-15 }, , T are the temperat, 0°C and 1 °C, then, , To = 273'15 + 0=273-15Kk, 1227315 ey, , 3), , ures on Kelvin scale, , Let Ty and, Corresponding to, , , , of gas, An, ¥ } ies P=constant, it P=constant, y T(K) —> 0 VorT —>, (a) (b), , , , , , , , , , , y Joseph Gay Lussac. It gives a, n€_pressure and temperature at constant, , At constant volume, the pressure of gives mass of the gas, directly proportional to its absolute temperature., , i.e. P « T (at constant volume), , , , , Aliter, It states that if volume is kept constant, the pressure of, , given mass of a gas increases or decreases by, , , , ras, , pressure at 0° C for each 1°C rise or fall of temperature., , Let the pressure of the given mass of gas at 0°C and fC, are Po and P, then according to Gay Lussac’s law, , Pivipe fgay t =», (7B), By 01 gags) OA 27815, , . T, << OY kia Rs, , , , , , where Ty (K) = 273'15 and T(K) =273:15 +f, , cS 5 =

Page 3 : ° POSE ERE, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Fe ai For n moles of gas, Py T, PV = »RT, : This is perfect gas equation, = =Gonstent or Pet. The ideal gas equation is often Expresseq |, on as number of molecules, N. Mtg, raphica ; =, e N =n Ng where Na ~ Avogadtoy, N, P P V=constant oo lied Ne, f v i, eee Thus eqn. (5) becomes, ile anl{ ik, 0 —>T 0 Port —> PV (ar yRt=§( 2), eek Fig. 3 ", _ 3(_PERFECT GAS EQUATIONIDEALGASEQUATION =») /, - Ro, _The three laws just described may be combined into one eal eo Mee or., on, resulting in the ideal gas equation. . PV =NkpT, ider one mole of a perfect gas. Let P;, Vj, Tj, and P2, | Universal Gas Constant (R), the initial and final pressure, volume and temperature, , § respectively. Suppose the initial state changes to The-ideal gas equation for n moles is, , two steps. PV =nRT, : Suppose initially the temperature T, of the gas is PV, , a, , tant. Now let the pressure of the gas is changed from R=— => eee ome, e nT /Number of moles x temperature, , c h at the volume changes from V, and Y, ., | Work done, , , , n according to Boyle’s law R=, 4 number of moles x temperature, ss ri) YN,, PV) = P,V; so V, = at will) So the universal gas constant represents the amott, . B work done by-or-en-the gas per mole per kelvin., , Il ] Now suppose the pressure P, of the gas i net S.1. Unit of R = J mol!K"!, Tere ' he temperature of the gas changes from T, an CGS. Unit of R= cal mol? C", , m vi to V2 Value of R : Consider one mole of the gas at §.1F, anasto *s law, 0 Charle’s P)Vo, , , , apenas VT, eo) a R Ty, : 3 : Py = 0°76 m of Hg column, , | = 0:76 x 13:6 x 103 x 9:8 Nm”, Ty (Standard temperature) = 273 15K, Vo = Volume of 1 mole of gas at 6.TP., , = 70-4 litre = 22-4 x 103 m’, , , , j, 3y (0, 0:76 x 13:6 x 9:8 x 22-4 x 10, , , , , , so R 27315, m, (3) ( R =8-31J mol! K7 in S. ye, a ant has same value for In C.G.S. system, onstant (R). 8-31 onthe, oS =e molt °C, 4 Re, R = 1:98 cal mol! °C”, , (4)

Page 4 : ¥ OF GASES, , A matter is made up of molecules. The molecules of a gas, are in state of continuous motion. Their velocities depend on, temperature. Using the motion of molecules, various properties, of gas like pressure, temperature and energy are calculated, Hence this theory was called as kinetic theory of gases,/which, was given by Clausius and Maxwell., , 6. (MAIN POSTULATES OF KINETIC THEORY OF, ‘GASES, A gas is a collection of large number of molecules., These molecules are perfectly elastic, identical and hard, spheres. The molecules of gas are so small that the, , volume of a molecule is negligible as compared to, ___Nolume of gas. |, j 2. The molecules are always in random motions, so they, _ are not having any specific direction., AB. The molecules travel in straight line and are in free, ‘motion most of the times. The time interval of collision, “between any two molecules is very small., , > collision between the molecules and walls of the, wtainer is purely elastic. So kinetic energy and, entum are conserved., ‘travelled by a molecule between two successive, yns is called free path and mean distance travelled, olecule between two successive collisions is called, any 4 e path. ae, , ion of molecules is governed by Newton’s laws, , vt a, , a, , , , , , , , , , , , , 4 OT, , The effect of gravity on the motion of molecules is, , , , , , E EXERTED BY GAS, , is filted-inra Cubical container having, er consists of ‘n’ molecules and the, otion., , Area of container (A) =/ «1 =, Volume of container (V) = 7, , Consider one molecule of mass (m), movin, Cy. Let uw, vy, w; are components of velocity, z axis., , 8 With ve., , along x, y a, Momentum of molecule as it goes from face A, B=mu ” te, As the collision is perfectly elastic, the molecule ;., , with same velocity. Obviously y and z components of ved, do not change in the collision, but x - component of ye lo, i, , reversed. So velocity of molecule after collision is (- 4 i., 5 A i}, , + Momentum of molecule after collision with face pChange in momentum of the molecule = Final mo |, — initial Momenty,, dp, =— mu,— mu, =—2 mu fy, As the momentum of the system is conserved,, momentum imparted to the wall in each collision = 2mu, 19, , Time taken by the molecule in travelling from face 4y, face B and then back to face A., , , , , , , , , , , , , , , , Velocity = a, time, dt = 2k 1+!, u Hol edt, , Force exerted by the molecule on wall of container, , , , dp, F = x, “ihe hide, _ 2mhy 2m uy m uy, F = _ Fo =, Pile 2hl wy 21 l, As there are n molecules of the gas moving with vanes, Ci Op sane C,,. Therefore total force exerted by gas on fae, of container, Poy, t+ Fo, + .........- |e, Eel oy Put, = ] uy, + ] Uy Pi sic vise i n, m 2 2 2 |, F, =| Wty tee Yn, i ;, .. Pressure exerted by the gas molecules along X™, ee ey? + ainiecar® +r), , o, cules, Similarly the pressure exerted by the 24° mole, , walls of container along Y and Z axis, , 2, m D 2 uv.), , coe cy wt, Mm 7:2 2 +0), , =, +, 5, re, , a Pp

Page 5 : eeeee, veers, , eeeee, , R ed of gas molecules and C j4, , speed of gas molec, , ria) because area (A), pear in final result, , yessel/container is t, accordance with Pase |, , Multiply and divide 2.1.5, of this equation by, ie, , a, , a, 5 Pe, , Pp =, 2, , «—E, ’ 3, , bein, Es 7 PC" = average kinetic energy per unit, , e of gas, : a Average K.E, 3 Volume, , z 3, 5 or a., , aVverag otic energy per unit volume of gas is, , Or, rhe_pressure exerted by a gas is two, Kinetic energy per untt-verwme-of Gasman, KINETIC INTERPRETATION OF T, According to kinetic theory of gases, the, sy 1 mole of an ideal gas is given by, , ird of the average, , —o™ @, , rt, , sar, , heme =, , pressure P exerted, , (1), , But PV = RT (For one mole of gas), 3RT, , —_—_—, , M, , C= (ee js root mean square velocity of molecules, , M =mN, , RT = = MC? 2c =