Q.What is molar specific heat capacity? For a monatomic gas, calculate the molar specific heat capacity at constant volume (Cv), the molar specific heat capacity at constant pressure (Cp), and the adiabatic ratio (γ).
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Start your 14-day free trial to unlock the full solution →Molar specific heat capacity is heat needed per mole per kelvin; for a monatomic gas, using the equipartition theorem with 3 translational degrees of freedom, Cv = (3/2)R, Cp = Cv + R = (5/2)R, and γ = Cp/Cv = 5/3.
Molar specific heat capacity, C, is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree (kelvin or celsius). It depends on the conditions under which heat is supplied — commonly at constant volume (Cv) or constant pressure (Cp).
For a monatomic ideal gas (like helium, argon, neon): a monatomic molecule (treated as a point particle) has only translational kinetic energy, along 3 independent directions (x, y, z) — i.e. 3 translational degrees of freedom, and no rotational or vibrational degrees of freedom (a point mass can't meaningfully rotate about its own axis).
By the law of equipartition of energy, each degree of freedom contributes (1/2)RT to the internal energy per mole, so the total internal energy of 1 mole of a monatomic gas is:
U = 3 × (1/2) R T = (3/2) R T
Molar specific heat at constant volume, Cv = dU/dT (at constant V):
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