In this problem we use the following result. If heat is added to a system that has a constant heat capacity C, raising the absolute temperature from T_i to T_f, the change in entropy of the system is Delta S = integral dQ/T = integral_T_i^T_f CdT/T = C ln (T_f/T_i) Two identical blocks of aluminum, each with C = 300 J/K, start out at absolute temperatures 300 K and 400 K. They are put into thermal contact but are otherwise isolated. Intuitively, we can see that they both end up at 350 K, the temperature exactly halfway in between. How much heat is transferred in the process? What is the entropy change for each block? What is the overall entropy change for the whole system?
(a). Heat transferred in this process = C dt
= (300 J/K) (350 K - 300 K)
= 300 J/K (50 K)
= 15000 J
(b). The entropy change for first block dS = C ln (350/300)
= 300 ln(1.1666 )
= 300(0.1541)
= 46.24 J/K
The entropy change for second block dS \' = C ln (350/400 )
= 300 ln(0.875 )
= 300(-0.13353)
= -40.059 J/K
(c).The overall entropy change for the whole system = dS+dS\'
= 46.24 +(-40.059)
= 6.181 J/K
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