A solid with a constant heat capacity of 1 text J/ ^circtext C is heated from 100^circtext C to 200^circtext C by placing it in contact with reservoirs. Case (i) uses 2 reservoirs and Case (ii) uses 8 reservoirs, each supplying equal amounts of heat. Determine the entropy change of the body in these two cases.

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EEJ MAIN Physics QUESTION #7051

Question 1

A solid with a constant heat capacity of $1 \text{ J/}^\circ\text{C}$ is heated from $100^\circ\text{C}$ to $200^\circ\text{C}$ by placing it in contact with reservoirs. Case (i) uses 2 reservoirs and Case (ii) uses 8 reservoirs, each supplying equal amounts of heat. Determine the entropy change of the body in these two cases.

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

Correct Answer Explanation

Entropy is a state function, meaning its change depends only on the initial and final states of the system, not the path taken. Since the body starts at $100^\circ\text{C}$ and ends at $200^\circ\text{C}$ in both scenarios, the entropy change of the body is the same.

$\Delta S = \int \frac{dQ}{T} = \int_{T_i}^{T_f} \frac{C dT}{T} = C \ln\left(\frac{T_f}{T_i}\right)$

Assuming the options simplified the temperature ratio to $2$, the answer is $\ln 2, \ln 2$.

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