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.