Discussion
10 kg of water at 300 K is poured into a bucket containing 10 kg of water at 350 K. Heat capacity of water is 4.2 kJ/kg.K. Neglecting any heat losses to the surroundings, the change in the entropy (in kJ/K) of the system during this process (rounded off to two decimal places) is
Answer: B
The entropy change is 0.25 kJ/K.
Equal masses of water mix to the mean temperature, 325 K. The entropy change of each mass is \(mc\ln(T_f/T_i)\):
\[ \begin{aligned} \Delta S &= 42\left[\ln\tfrac{325}{300} + \ln\tfrac{325}{350}\right] \\ &= 42(0.08004 - 0.07411) \\ &= 0.249 \approx 0.25\ \text{kJ/K} \end{aligned} \]
with \(mc = 10 \times 4.2 = 42\) kJ/K. The cold water gains more entropy than the hot water loses, so the total is positive, as it must be for an irreversible mixing. 0.00 would describe a reversible process, and 0.50 and 0.75 overstate the result.
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