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  4. 1 mole of an ideal gas at STP is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy (γ = 1.4)

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Q. $ 1 $ mole of an ideal gas at $ STP $ is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy $ (\gamma = 1.4) $

Thermodynamics

Solution:

For adiabatic expansion
$ T_{1}V_{1}^{\gamma-1} =T_{2}V_{2}^{\gamma-1} $
$ T_{2} = T_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1} =273 \left(\frac{1}{2}\right)^{1.4-1} $
$ \simeq 206\,K $
$ dU=dW = \frac{R}{\gamma-1} \left(T_{1}-T_{2}\right) $
$ =\frac{ 1\times8.31}{\left(1.4-1\right)}\left(273-206.89\right) $
$ \simeq 1373\,J $