Question

4. The following equation of state for 1 mole of a real gas is proposed: RT a P = V-bT RTV2 where a and b are constants characteristics of the gas. (a) What is the relation between the Boyle temperature (B) and the critical temperature (Tc)? (b) For the real gases following above equation of state, show that the maximum attractive interaction between gas molecules is located 2 - Tp in P, 1 under the condition of temperature, 3 irrespective of the identity of the gas

Answer 1

- A. The following equation of state for Imole of a real gas is proposed: P R I - a to co kere was bome corotondo. RT P = coro. rando are a RT v2 a, b where V-bT of (P+) (v-b) =RT - 0 at critical teaping point of infection appears. also appeared point to V From voor verb 2764

(Peq) (w w 3RD V-6 so sis Rt (v-b)" - 4 p p = RJ ( 1 - 2 - 1 - 2 Pre Rt (1- & b) - - clo Prz Rt + Rtbuat at Bryle's temp To PUERT pr & RT + (RTb-a). pe bhp RT Empirically, рvv @ A Вре с. -- d at Boyle's terp B=0 Therefore Rb-a=0 By Hotel

from @ from Teatro 27Rb now, for from the po per tot querten - de dv za Фртуз (-67) 72 2T (v-bt) 2 Rtv3 ZRT - 68a - RTVA so ar 3 (V-bt) 3 = Rť Rt v4 (V-bt) 3 = 3 0 = @ » v-bt ») et une from o btc RTc 4b7c² t 27 (6 Tel = TC 3 27 62 R² W 27582