Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynum'ca 69

Fig. 1.25.
(c) We construct the V(Vo1tage)-q(charge) diagram for the cycle as
shown in the Fig. 1.25. We have

W= Vdq.

Assume V2 = V, + dV, where dV is an infinitesimal voltage change, and let

the capacitance of the capacitor be C(T). We then have

f

0 -+ A : V = q/C(T1) , B -+ C : V = q/C(T2)

Obviously the adiabatic line B -+ C crosses point 0. Thus if dV is.a small

quantity, V3 is also a small quantity. Then in the first-order approximation,