Every gas consists of a large number of small particles called molecules moving with very high velocities in all possible directions.
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1 Kietic thery f gases ( Kietic thery was develped by Berlli, Jle, Clasis, axwell ad Bltzma etc. ad represets dyamic particle r micrscpic mdel fr differet gases sice it thrws light the behir f the particles (atms ad mlecles which cstitte the gases ad cat be see. Prperties f gases which we stdied earlier are part f macrscpic mdel. ( Pstlates (i (ii (iii (iv (v (vi (vii Every gas csists f a large mber f small particles called mlecles mvig with very high velcities i all pssible directis. The vlme f the idividal mlecle is egligible as cmpared t the ttal vlme f the gas. Gases mlecles are perfectly elastic s that there is et lss f kietic eergy de t their cllisis. The effect f grity the mti f the mlecles is egligible. Gases mlecles are csidered as pit masses becase they d t psses ptetial eergy. S the attractive ad replsive frces betwee the gas mlecles are egligible. The pressre f a gas is de t the ctis bmbardmet the walls f the ctaiig vessel. At cstat temperatre the erage K.E. f all gases is same. Page
2 (viii The erage K.E. f the gas mlecles is directly prprtial t the abslte temperatre. (3 Kietic gas eqati : O the basis f abve pstlates, the fllwig gas eqati was derived, PV m 3 where, P = pressre exerted by the gas, V = vlme f the gas, m = erage mass f each mlecle, = mber f mlecles, = rt mea sqare (RS velcity f the gas. (4 Calclati f kietic eergy We kw that, K.E. f e mlecle m K.E. f mlecles 3 PV m 3 ( PV m =, The K.E. f mle gas 3 RT ( PV RT T.47 T Jles. Average K.E. per mle 3 RT 3 KT N(Avgadr mber N R K Bltzma cstat N Page
3 This eqati shws that K.E. f traslati f a gas depeds ly the abslte temperatre. This is kw as axwell geeralisati. Ths erage K.E. T. If T 0K (i.e., 73.5 C the, erage K.E. = 0. Ths, abslte zer (0K is the temperatre at which mleclar mti ceases. (5 Kietic gas eqati ca be sed t establish gas laws. Examples based Kietic mleclar thery f gases Example : The kietic eergy fr 4 grams f itrge gas at 7 C is early (ml. mass f itrge = 8 ad gas cstat = 8.3JK ml (a.0 J (b 4.5 J (c 493 J (d 3.3 J Slti: (c K.E. 3 RT ml r K.E. RT J 493 J 8 Page3
4 leclar cllisis ( The clsest distace betwee the cetres f tw mlecles takig part i a cllisi is called mleclar r cllisi diameter (. The mleclar diameter f all the gases is early same lyig i 8 the rder f 0 cm. leclar diameter ( The mber f cllisis takig place i it time per it vlme, called cllisi freqecy (z. (i The mber f cllisi made by a sigle mlecle with ther mlecles per it time are give by, ZA. where is the mber f mlecles per it mlar vlme, Avgadr mber(n 6.00 V m 3 m 3 (ii The ttal mber f bimleclar cllisi per it time are give by, ZAA. (iii If the cllisis ivlve tw like mlecles, the mber f bimleclar cllisi are give by, ( A B ZAB AB 8 RT A B / Page4
5 where, ( mn 0 A B AB ad A, B are mleclar weights (iv (a At particlar temperatre; Z p (b At particlar pressre; Z T 3/ (c At particlar vlme; Z T / (3 Drig mleclar cllisis a mlecle cvers a small distace befre it gets deflected. The erage distace trelled by the gas mlecles betwee tw sccessive cllisi is called mea free path (. Average distace trelled per it time( N. f cllisis made by sigle mlecle per it time (Z A r. (4 Based kietic thery f gases mea free path, T. Ths, P (i Larger the size f the mlecles, smaller the mea free path, i.e., (radis (ii Greater the mber f mlecles per it vlme, smaller the mea free path. (iii (iv Larger the temperatre, larger the mea free path. Larger the pressre, smaller the mea free path. Page5
6 (5 Relati betwee cllisi freqecy (Z ad mea free path ( is give by, Z leclar speeds r velcities ( At ay particlar time, i the give sample f gas all the mlecles d t pssess same speed, de t the freqet mleclar cllisis with the walls f the ctaier ad als with e ather, the mlecles mve with ever chagig speeds ad als with ever chagig directi f mti. ( Accrdig t axwell, at a particlar temperatre the distribti f speeds remais cstat ad this distribti is referred t as the axwell-bltzma distribti ad give by the fllwig expressi, d 0 3/ / RT 4.e. dc RT where, d0 Nmber f mlecles t f ttal mber f mlecles, hig velcities betwee c ad c dc, d0 / Fracti f the ttal mber f mlecles, = mleclar weight, T = abslte temperatre. The expetial factr / RT e is called Bltzma factr. (3 axwell ge distribti Ump crves f mleclar speeds fr CO Fracti f mlecles 300 K (T T<T<T3 Ump 500 K (T U U Ump 800 K (T3 Page6 leclar speed
7 at differet temperatres. Special featres f the crve are : (i (ii (iii Fracti f mlecles with tw high r tw lw speeds is very small. N mlecles has zer velcity. Iitially the fracti f mlecles icreases i velcity till the peak f the crve which pertais t mst prbable velcity ad thereafter it falls with icrease i velcity. (4 Types f mleclar speeds r Velcities : (i Rt mea sqare velcity ( : It is the sqare rt f the mea f the sqares f the velcity f a large mber f mlecles f the same gas PV ( RT ( RT kt P mn mn m d 0 0 where k = Bltzma cstat R N 0 (a (b Fr the same gas at tw differet temperatres, the rati f RS T velcities will be, T Fr tw differet gases at the same temperatre, the rati f RS velcities will be, (c RS velcity at ay temperatre t C may be related t its vale at S.T.P. as, t 3 P(73 t. 73d Page7
8 Nte : RS velcity explaied the -existece f gases i the atmsphere f m. Whe temperatre ale is give the, T cm/ sec. If P ad T bth are give, se eqati i te f temperatre, i.e., se 3RT ad t 3PV (ii Average velcity ( v : It is the erage f the varis velcities pssessed by the mlecles. v v v v3... v v 8RT 8kT m (iii st prbable velcity ( mp : It is the velcity pssessed by maximm mber f mlecles f a gas at a give temperatre. mp RT PV P d (5 Relati betwee mleclar speeds r velcities, (i Relati betwee ad v : v 0.93 r.085 v (ii Relati betwee mp ad : mp 0.86 r.4 mp (iii Relati betwee mp ad v : v.8 (iv Relati betwee mp, v ad : mp Page8
9 mp : v : RT : 8RT : 3RT : 8 : 3.44 :.595 :.73 :.8 :.4 i.e., mp v Examples based mleclar speeds Example : The velcity f CO at a temperatre T (i kelvi is x cm s. At what temperatre (i kelvi the velcity f itrs xide wld be 4x cm s (a 6 T (b T (c 4 T (d 3 T Slti: (a 3RT T CO CO N O T N O CO N O i.e., x T 44 r 4x 44 T N O T r 4 T N O TN O 6 T Page9
10 Example 3 : velcity at The velcity f a ideal gas at 97 C (i ms is 7 C is 0.3 ms. Its (a 3.0 (b.4 (c 0.9 (d 0.6 Slti: (d 3RT Fr the same gas at tw differet temperatres, T ; T , ms Example 4 : The velcity f hydrge is 7 times the velcity f itrge. If T is the temperatre f the gas (a T(H T(N (b T(H T(N (c T(H T(N (d T(H 7T(N Slti: (c 3RT (H T(H (N ; r (N (H T(N 7 T(H 8 T(N r T(H T(H 7 4 r r T(N T(H T(N T(N i.e., T(N T(H Example 5 : If the erage velcity f N mlecles is 0.3 m/s at 7 C, the the velcity f 0.6 m/s will take place at (a 73 K (b 97 K (c 000 K (d 00 K Page0
11 Slti: (d v 0.9 v T v T r 0.6 T 300 r T K T Example 6 : The temperatre f a ideal gas is redced frm 97 C t 7 C. The velcity f the mlecles becmes (a Dble the iitial vale (b Half f the iitial vale (c Fr times the iitial vale (d Te times the iitial vale Slti: (b 3RT T T Page
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