57. We use the first law of thermodynamics: ∆E
int
= Q
− W . The change in internal energy is ∆E
int
=
nC
V
(T
2
− T
1
), where C
V
is the molar heat capacity for a constant volume process. Since the process is
adiabatic Q = 0. Thus, W =
−∆E
int
= nC
V
(T
1
− T
2
).