An adiabatic process is performed on 15 moles of an ideal gas (γ = 1.44). What is the heat capacity at constant pressure for the gas? Let the ideal-gas constant R = 8.314 J / (mol • K).

25 J / (mol • K)

27 J / (mol • K)

31 J / (mol • K)

23 J / (mol • K)

29 J / (mol • K)

27 J / (mol • K)

Explanation:

γ = Cp / Cv

We're given γ and we need to find Cp (heat capacity at constant pressure) per mole. First we need to find Cv (heat capacity at constant volume). Cv is defined as:

Cv = Cp - nR

where n is the number of moles and R is the ideal gas constant.

So:

γ = Cp / (Cp - nR)

γ (Cp - nR) = Cp

γ Cp - γnR = Cp

(γ - 1) Cp = γnR

Cp / n = γR / (γ - 1)

Given γ = 1.44 and R = 8.314 J/mol/K:

Cp / n = (1.44) (8.314 J/mol/K) / (1.44 - 1)

Cp / n = 27 J/mol/K