1. Δ S = nRln(p_i/p_f) 2. Δ S = nRTln(p_f/p_i) 3. Δ S = RTln(p_i/p_f) 4. Δ S = nRln(p_f/p_i)

Answer: 1. Δ S = nRln(p_i/p_f) Key idea: for an isothermal ideal gas, Δ S=nRln(V_f/V_i) , and V∝1/p . Δ S=nRlnV_f/V_i=nRlnp_i/p_f The T does not appear, which rules out options with RT .

Topic: Second law, entropy and spontaneity· Chemical Thermodynamics

For a sample of perfect gas when its pressure is changed isothermally from p_i to p_f, the entropy change is given by

1. $\Delta S = nR\ln\left(\frac{p_i}{p_f}\right)$

2. $\Delta S = nRT\ln\left(\frac{p_f}{p_i}\right)$

3. $\Delta S = RT\ln\left(\frac{p_i}{p_f}\right)$

4. $\Delta S = nR\ln\left(\frac{p_f}{p_i}\right)$

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Answer: 1. $\Delta S = nR\ln\left(\frac{p_i}{p_f}\right)$

Key idea: for an isothermal ideal gas, $\Delta S=nR\ln(V_f/V_i)$, and $V\propto1/p$.

$$\Delta S=nR\ln\frac{V_f}{V_i}=nR\ln\frac{p_i}{p_f}$$

The $T$ does not appear, which rules out options with $RT$.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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For a sample of perfect gas when its pressure is changed isothermally from p_i to p_f, the entropy change is given by

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