Problems and Solutions on Thermodynamics and Statistical Mechanics

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