In physical chemistry, it is shown that the pressure P of a gas is related to the volume V and temperature T by van der Waals’ equation:

where a, b, n, and R are constants. The critical temperature T_c of the gas is the highest temperature at which the gaseous and liquid phases can exist as separate phases.

a. When T = T_c, the pressure P is given as a function P(V) of volume alone. Sketch the graph of P(V).

b. The critical volume V_c is the volume for which P'(V_c) = 0 and P"(V_c) = 0. Show that V_c = 3b.

c. Find the critical pressure Pc = P(V_c) and then express Tc in terms of a, b, n, and R.

Transcribed Image Text:

P + a)(v. (V - b) = nRT