A solid object with a constant heat capacity of 1 text J/ ^circtext C is heated from 100^circtext C to 200^circtext C . In Case A, it is placed in contact with 2 reservoirs sequentially. In Case B, it is placed in contact with 8 reservoirs sequentially. What is the entropy change of the body in these two cases respectively?

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EEJ MAIN Physics QUESTION #7069

Question 1

A solid object with a constant heat capacity of $1 \text{ J/}^\circ\text{C}$ is heated from $100^\circ\text{C}$ to $200^\circ\text{C}$. In Case A, it is placed in contact with 2 reservoirs sequentially. In Case B, it is placed in contact with 8 reservoirs sequentially. What is the entropy change of the body in these two cases respectively?

$\ln 2, 4\ln 2$
$\ln 2, \ln 2$✔️
$\ln 2, 2\ln 2$
$2\ln 2, 8\ln 2$

Correct Answer Explanation

Entropy is a state function. This means the change in entropy depends only on the initial and final states of the system, not on the path or the number of intermediate steps taken to reach that state.

Since the body is heated from an initial temperature $T_1 = 373 \text{ K}$ to a final temperature $T_2 = 473 \text{ K}$ in both cases, the entropy change $\Delta S$ of the body will be identical in both scenarios.

$\Delta S = \int \frac{dQ}{T} = \int_{T_1}^{T_2} \frac{ms dT}{T} = C \ln \left( \frac{T_2}{T_1} \right)$.

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