Question

05. Using the Dieterici equation of state, RT p= a/RTV V - b show that a Pc a 4e2b2 Vc - 25, TC = 4Rb

Answer 1

ANSWER :
The Dieterici equation of state is RT alRtv given by P= V-b Now, taking tog on both sides of the equation. logp = log [ A le-alRtv =log [ - ] + log (e alRTV). logp= log RT - dog (u-b) + (-a/RTV) partial De fterentral equation with respect to v [as Rand are constants) a ㅗ 0 I de P dv v-b RTV 2 1 9 де Plut Rive] dv JP Taking at constant t=0 as f(VC, Tc)=0 - dv + Ple+ verb alue-o [Come bi haute het RTV 2 29 RT v3 again differentiating egn with respect to vo de fe pot apve]+platbyen

© Taking up have du we =0 and dep dre 29 Cuc-b? RTV² =0 dvelt locita (verb) ratio and we have of 2 29 RTV² Now, squaring en 6 and ta taking [b] R22 VY e-bJ RTVS ܢܘܘ a 2 RTV a=&R TV putting these value of a in eqn we have -2 RTVE Ne-b VR 2 VC verb V ca v-2b. :. [vc=26 puting the value of vineano Pc RT е 2 RTV Rtv 2b-b

3 Pc = again, RT = 9 RT b е 2v ub PE which gives ub2e2 Pc 46²2 peetting the va value and of Pc ve in equation a RTC 2b-b 2-2 419 2 KT ubre 2 beer RTC a 17 ub²e2 be ? .a ць R