What is the relationship between the heat capacity at constant pressure (Cp) and the heat capacity at constant volume (Cv) for one mole of an ideal gas (Mayer's relation)?
Answer and explanation
Correct answer: D. Cp - Cv = R
- Step 1: For an ideal gas, internal energy depends only on temperature, so .
- Step 2: Enthalpy is defined as (for 1 mole).
- Step 3: Differentiating with respect to temperature gives: .
- Step 4: Since and , substituting yields Mayer's relation: .
Answer
Cp - Cv = R
Why not the others: 'Cv - Cp = R' reverses the terms (since due to expansion work at constant pressure, ); 'Cp / Cv = R' confuses the difference with the adiabatic index ; 'Cp + Cv = R' has incorrect dimensions and algebra.
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