57. The change in entropy in transferring a certain amount of heat Q from a heat reservoir at T
1
to another
one at T
2
is ∆S = ∆S
1
+ ∆S
2
= Q(1/T
2
− 1/T
1
).
(a) ∆S = (260 J)(1/100 K
− 1/400 K) = 1.95 J.
(b) ∆S = (260 J)(1/200 K
− 1/400 K) = 0.650 J.
(c) ∆S = (260 J)(1/300 K
− 1/400 K) = 0.217 J.
(d) ∆S = (260 J)(1/360 K
− 1/400 K) = 0.072 J.
(e) We see that as the temperature difference between the two reservoirs decreases, so does the change
in entropy.