Question

100 g of water is slowly heated from 27◦C to 87◦C. The change in entropy of water is (Specific heat capacity of water = 4200 J/kg/K)

• A. 376.6 J/K
• B. 276.6 J/K
• C. 176.6 J/K
• D. 76.6 J/K

Hint:

Entropy changes for heating processes depend on the average temperature. When the temperature change is significant, always compute the average temperature or integrate to avoid underestimating or overestimating ∆S. This principle is vital in understanding thermodynamic efficiency.

Answer 1

The Correct Option is A

The change in entropy is given by:
\[\Delta S = \frac{Q}{T}\]
where \(Q = mc\Delta T\) and \(\Delta T = 87 - 27 = 60 \, \text{K}\). Substituting \(m = 0.1 \, \text{kg}\), \(c = 4200 \, \text{J/kg/K}\):
\[Q = 0.1 \times 4200 \times 60 = 25200 \, \text{J}\]
For average \(T\),
\[\Delta S \approx \frac{25200}{333 \, \text{K}} \approx 376.6 \, \text{J/K}\]