Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodynamics 59

Hence
W 2 Cu(Tl - To) - CUT, ln(Tl/To) = Wmin.

With the inclusion of vibrational degrees-of-freedom, Wmin increases as C,
increases.

1064
A reversible heat engine operates between two reservoirs, Ti and T2
(T2 > Tl). Ti can be considered to have infinite mass, i.e., Ti remains
constant. However the warmer reservoir at Tz consists of a finite amount
of gas at constant volume (p moles with a specific heat capacity C,).
After the heat engine has operated for some long period of time, the
temperature Tz is lowered to TI.
(a) What is the heat extracted from the warmer reservoir during this
period?
(b) What is the change of entropy of the warmer reservoir during this
period?
(c) How much work did the engine do during this period?
(Columbia)
Solution:
(a) Qab = pC,(T, - Ti).
dQ GUdT Tl
T T Tz

(b) Because dS = - = ___ , AS=pC,ln-.

(c) dW - = 1 - - Tl

dQ T’

dQ = -pC,dT, therefore the work done by the

engine is

W=/dW=-/TT1 (1- ~)pCudT=pC,(T2-4))LC,Tll~ (2) *

1065

Large heat reservoirs are available at 900 K (H) and 300 K (C).

(a) 100 cal of heat are removed from the reservoir H and added to C.

(b) A reversible heat engine operates between H and C. For each

What is the entropy change of the universe?