Heat Capacity Ratio

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For ideal gas, Cp - Cv equals?

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1. **Mayer's Relation**: For an ideal gas, the molar heat capacity at constant pressure ($C_p$) and at constant volume ($C_v$) are related by the universal gas constant ($R$).
2. **Derivation**: From enthalpy $H = U + PV$. For an ideal gas $PV = RT$, so $H = U + RT$.
3. **Differentials**: $dH = dU + R dt \implies C_p dT = C_v dT + R dT$.
4. **Result**: Dividing by $dT$ gives **$C_p - C_v = R$**.
5. **Significance**: This holds true for any ideal gas, regardless of its atomicity or molecular structure.

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Heat Capacity Ratio

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