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