Question

2 moles of an ideal monatomic gas is carried from a state \(\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)\) to a state \(\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)\) along a straight line path in a \(P-V\) diagram. The amount of heat absorbed by the gas in the process is given by
(A) \(3 \mathrm{P}_{0} \mathrm{~V}_{0}\)
(B) \(\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}\)
(C) \(6 \mathrm{P}_{0} \mathrm{~V}_{0}\)
(D) \(\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}\)

Answer 1

Ans(C)
\(\Delta \mathrm{U}=\mathrm{n} C_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{n} \frac{3 \mathrm{R}}{2}\left(\frac{4 \mathrm{P}_{0} \mathrm{~V}_{0}}{\mathrm{nR}}-\frac{\mathrm{P}_{0} \mathrm{~V}_{0}}{\mathrm{nR}}\right)=\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}\)

\(\mathrm{W}=\left(2 \mathrm{P}_{0}+\mathrm{P}_{0}\right) \frac{\mathrm{V}_{0}}{2}=\frac{3 \mathrm{P}_{0} \mathrm{~V}_{0}}{2}, \Delta \mathrm{Q}=\mathrm{W}+\Delta \mathrm{U}=6 \mathrm{P}_{0} \mathrm{~V}_{0}\)

Answer 2

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Answer 3

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