62 Problems €4 Solutions on Thermodynamics €4 Statistical Mechanics
Solution :
(a) In the cycle, the heat absorbed by the engine is
400 + 300
2
Q = (1000 - 500) = 1.75 x lo5 J ,
and the work it does is
400 - 300
2
W = (1000 - 500) = 2.5 x lo4 J
Thus the efficiency is q = W/Q = 14.3%.
fore
(b) Obviously the equilibrium temperature is T3 = (TI +T2)/2. There-
and
thus
Since (TI + T2)2 2 4TlT2, we have AS 2 0.
1068
(a) One mole of an ideal gas is carried from temperature TI and molar
volume V1 to T2,VZ. Show that the change in entropy is
T2 v2
Ti Vl
AS=C,ln-+Rln-.
(b) An ideal gas is expanded adiabatically from (pl, Vl) to (p2, V2).
Then it is compressed isobarically to (p2, V1). Finally the pressure is