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25 June, 21:14

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)

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  1. 25 June, 21:28
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    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
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