Specific-Heat Calculator with Variable γ

For an ideal gas, vary the heat-capacity ratio γ and see how the molar heat capacities at constant volume and constant pressure are related.

Heat-capacity ratioγ = 1.400
CV20.79 J mol⁻¹ K⁻¹
CP29.10 J mol⁻¹ K⁻¹
CP − CV8.314 J mol⁻¹ K⁻¹
CP/CV1.400

Parameters

1.400
For an ideal gas, γ must be greater than 1.
1.00 mol
Used to compare heat required for the same temperature change.
50 K
Positive means heating; negative means cooling.
γ = CP/CV,    CP − CV = R
CV = R/(γ−1),    CP = γR/(γ−1)
At γ = 1.40: CV ≈ 20.79 and CP ≈ 29.10 J mol⁻¹ K⁻¹. Constant-pressure heating requires more energy because the gas can also do expansion work.

Compare CV and CP

CV
20.79 J/mol·K
CP
29.10 J/mol·K
Difference
R = 8.314
Constant volume 1.04 kJ QV = nCVΔT. No boundary expansion work for a rigid container.
Constant pressure 1.46 kJ QP = nCPΔT. More heat is required for the same ΔT.
Extra heat at constant pressure: QP − QV = nRΔT = 0.42 kJ.
Predict before moving γ

Decrease γ toward 1. What happens to CV and CP?

How CP and CV depend on γ

γ J mol⁻¹ K⁻¹ γ = 1.40 Cᵥ Cₚ
Important behavior: As γ approaches 1 from above, both heat capacities become large. Their difference remains exactly R in this ideal-gas model.
CV CP CP − CV = R