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Comprehension
Entropy is a state function and its value depends on two or three variables temperature (T), pressure \( (\mathrm{P}) \) 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 \( (\Delta S) \) according to the expression, \( \Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S} \) at a temperature \( \mathrm{T} \).
What would be the entropy change involved in thermodynamic expansion of 2 moles of a gas from a volume of \( 5 \mathrm{~L} \) to a volume of \( 50 \mathrm{~L} \) at \( 25^{\circ} \mathrm{C} \) ? [Given \( \mathrm{R}=8.3 \mathrm{~J} / \mathrm{mole} \mathrm{K} \) ]
(a) \( 38.23 \mathrm{~J} / \mathrm{K} \)
(b) \( 26.76 \mathrm{~J} / \mathrm{K} \)
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(d) \( 28.23 \mathrm{~J} / \mathrm{K} \)
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