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Comprehension
Entropy is a state function and its value depends on two or three variables temperature (T), pressure (P) and volume (V). Entropy change for an ideal gas having number of moles (n) can be determined by the following equation.
\[
\begin{array}{l}
\Delta \mathrm{S}=2.303 \mathrm{nC}_{\mathrm{V}} \log \left(\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\right)+2.303 \mathrm{nR} \log \left(\frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\right) \\
\Delta \mathrm{S}=2.303 \mathrm{nC}_{\mathrm{p}} \log \left(\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\right)+2.303 \mathrm{nR} \log \left(\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}\right)
\end{array}
\]
Since free energy change for a process or a chemical equation is a deciding factor for spontaneity, which can be obtained by using _entropy change ( \( \Delta \mathrm{S} \) ) according to the expression, \( \Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S} \) at a temperature \( \mathrm{T} \).
An isobaric process having one mole of an ideal gas has entropy change \( 23.03 \mathrm{~J} / \mathrm{K} \) for the temperature range \( 27^{\circ} \mathrm{C} \) to \( 327^{\circ} \mathrm{C} \). What would be the molar specific heat capacity \( \left(\mathrm{C}_{\mathrm{V}}\right) \) ?
(a) \( \frac{10}{\log 2} \mathrm{~J} / \mathrm{K} \mathrm{mol} \)
(b) \( \frac{10}{\log 2}-8.3 \mathrm{~J} / \mathrm{K} \mathrm{mol} \)
(c) \( 10 \times \log 2 \mathrm{~J} / \mathrm{K} \mathrm{mol} \)
(d) \( 10 \log 2+8.3 \mathrm{~J} / \mathrm{K} \mathrm{mol} \)
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