Question

1. The following equation of state for 1 mole of a certain real gas is proposed: RT P = 1- Te-a/RTV where a and b are characteristic constants for the real gas. (a) Predict the critical compression factor, Z , for the real gas that is satisfied with above equation of state. (b) What is the relation between the Boyle temperature (TB) and the critical temperature (TC)?

Answer 1

- Answers сч" - easan, The ginen equin of state is V-b P = RI e a/RTVO where adbore constants Differenkating above equin with forgeal gan. respect to v at constant temperature, we get - a/URT -a/URT RT a (V-b) v²RT . - RT (V-b)² + - Cons) [at] At Critical state, - can") e r b] = 0 TRTL Vb

an - Again differentating equation ③ with respect to constant temp" give - - G + el va com] 12 utting the value of self from ean", weh 1 1- 29 VRT tp / I VART V 1 At critical condition caxil oss om te verkry or bus] = > (39); Conto] + Jao (alt=0 so first term will be zero. lor by

Dividing Eau by eaun@, we toe get. LE Vc 2 (Vc-b) - 2/ve-b) 2 V 2) 2 Vc - v = 2b 2) ve = 26] or other Subshitating the value of Ve in cau & we get (265 RTE (26-b) u 6² R Tc a = 2V REL b 2 u b RTL 2V, R z y VERTc 1 At critical condition eall ① becomes Pc = R Te e VVERT Verb Putting the values of To, vc from abone equations in equn ③ we get - Te = 2.26k 2VRT) THERE

Pon-ble zez e- 962 Pea ube can be expressed as Critical compression factor ne Z. - P. Ve RTL Putting the values of Prive & Te, we get 462,2 x 2b ze - 9 a R R. . ubR = 0.27067 1.389 = 0. 270 Answer 1.6h) since we know To = Å ; Boyle Tempe And we get Te krom ab- after solve the ginen eaun state is - Tea ubr ü t B which is the relation blu TefTB ob abone giren caun