Question

An ideal monatomic gas initially has a temperature of T and a pressure of p. It is to expand from volume V1 to volume V2. If the expansion is isothermal, what are thefinal pressure pfi and the work Wi done by the gas? If, instead, the expansion is adiabatic, what are the final pressure pfa and the work Wa done by the gas? Stateyour answers in terms of the given variables.

Answer 1

Isothermal:

P1V1 = P2V2
P2 = P1V1/V2

Work = PdV = (nRT/V)dV = nRTln(V2/V1)

Adiabatic:

P1V1^y = P2V2^y

y = cp/cv = 5/3

P2 = P1V1^(5/3)/(V2^(5/3))

T1V1^(y-1) = T2V2^(y-1)

T2 = T1V1^(2/3)/V2^(2/3)

W = U = (3/2)nRdT = (3/2)nR(T1V1^(2/3)/(V2^(2/3)) - T1)