One mole of an ideal gas expands from initial state (2T0, V0) to final state (T0, 2V0). The process of expansion is given by T=−T0V0V+3T0. Work done by the gas during the expansion is (T : temperature; V : volume)

w=∫pdvpVR=−T0VV0+3T0 ∴p=−RT0V0+3RT0V∴w=RT0(3ln⁡2−1)

One mole of an ideal gas expands from initial state (2T0, V0) to final state (T0, 2V0). The process of expansion is given by T=−T0V0V+3T0. Work done by the gas during the expansion is (T : temperature; V : volume)

w=∫pdvpVR=−T0VV0+3T0 ∴p=−RT0V0+3RT0V∴w=RT0(3ln⁡2−1)

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One mole of an ideal gas expands from initial state (2T₀, V₀) to final state (T₀, 2V₀). The process of expansion is given by $T = (- \frac{T_{0}}{V_{0}} V + 3 T_{0})$ . Work done by the gas during the expansion is (T : temperature; V : volume)

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3RT₀ ln2

RT₀ ln2

RT₀ (3ln2 – 1)

T₀ V₀

answer is C.

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$w = \int pdv$
$\begin{array}{l} \frac{pV}{R} = \frac{- T_{0} V}{V_{0}} + 3 T_{0} ∴ p = \frac{- {RT}_{0}}{V_{0}} + \frac{3 {RT}_{0}}{V} \\ ∴ w = {RT}_{0} (3 \ln 2 - 1) \end{array}$

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One mole of an ideal gas expands from initial state (2T0, V0) to final state (T0, 2V0). The process of expansion is given by T=−T0V0V+3T0. Work done by the gas during the expansion is (T : temperature; V : volume)

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One mole of an ideal gas expands from initial state (2T₀, V₀) to final state (T₀, 2V₀). The process of expansion is given by $T = (- \frac{T_{0}}{V_{0}} V + 3 T_{0})$ . Work done by the gas during the expansion is (T : temperature; V : volume)