Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodyam’ca 63

increased to p1 at constant volume Vl. Show that the efficiency of the cycle
is

r] = 1 - 7(V2/vl - l)/(Pl/P2 - 1) j

where 7 = C,/C,,.
(Columbia)

Solution:
1 1
T T

(a) From dS = -(dU + pdV) = -(C,dT + pdV) and

pV = RT ,

we obtain

T2 v2

Tl Vl

AS=C,ln-+Rln-.

(b) The cycle is shown in the Fig. 1.23.

A

adiabatic

p2

Vl

Fig. 1.23.

The work the system does in the cycle is

Because AB is adiabatic and an ideal gas has the equations pV = nkT and

C, = C, + R, we get