A gas is compressed from a volume of \(2\,m^3\) to a volume of \(1\, m^3\) at a constant pressure of \(100\, N/m^2\). Then it is heated at constant volume by supplying \(150\, J\) of energy. As a result, the internal energy of the gas

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(A) increases by \(250\, J\)

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Detailed explanation

As we know, \(\Delta Q=\Delta u+\Delta w\)

(Ist law of thermodynamics) \(\Rightarrow \Delta \mathrm{Q}=\Delta \mathrm{u}+\mathrm{P} \Delta \mathrm{v}\)

or \(150=\Delta u+100(1-2)\)

\(=\Delta u-100\)

\(\therefore \Delta u=150+100=250 \mathrm{J}\)

Thus the internal energy of the gas increases by \(250 \mathrm{J}\)

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