Question

A metal wire is in thermal contact with two heat reservoirs at both of its ends. Reservoir 1 is at a temperature of 554 K, and reservoir 2 is at a temperature of 392 K. Compute the total change in entropy arising from the conduction of 1243 J of heat through the wire. Please give your answer in units of J/K.

Answer 1

Temperature of hot reservoir 1, Th = 554 K

Temperature of cold reservoir 2, Tc = 392 K

Total heat transferred, Q = 1243 J

As we know that, by transferring heat the entropy of both reservoirs change. If we transfer heat Q to a system at constant absolute temperature T its entropy changes by:

∆S = Q/T

Similarly the entropy of a system decreases when heat is removed from it, i.e. Q is negative.

The total change of entropy or your arrangement can be found by taking the sum of the entropy change of hot reservoir and cold reservoir. The amount Q is removed from hot reservoir at Th and transferred to the cold reservoir at Tc. So the total entropy change of the two reservoirs is:

∆S = -Q/Th + Q/Tc

= Q∙(1/Tc - 1/Th)

= 1243J ∙ (1/392K - 1/554K)

= 1243 * (0.00255 - 0.00180) J/K

= 0.932 J/K (Answer)