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Answer: 2. \(C_P - C_V = R\)

Key idea: for one mole of an ideal gas, \(C_P\) exceeds \(C_V\) by exactly \(R\) (Mayer's relation).

At constant pressure, heat also supplies the work of expansion. Using \(H=U+PV=U+RT\) for one mole: \(\dfrac{dH}{dT}=\dfrac{dU}{dT}+R\), so \(C_P=C_V+R\), i.e. \(C_P-C_V=R\).

Options 1, 3 and 4 do not follow from this relation (the sum or product of heat capacities has no such meaning).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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