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Question

What is the molar specific heat capacity at constant pressure for a monatomic gas if C_v = 12.45 J mol⁻¹ K⁻¹ and R = 8.3 J mol⁻¹ K⁻¹ ?

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Explanation

**Zeroth law of thermodynamics** if two systems A and B each in thermal equilibrium with third C, then A and B in equilibrium with each other, defines temperature as property that is same for systems in thermal equilibrium, basis for thermometer, temperature scale, thermal equilibrium means no net heat flow, same temperature. C_p - C_v = R . C_p = C_v + R = 12.45 + 8.3 = 20.75 J mol⁻¹ K⁻¹ . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁), adiabatic P V^γ = const and η

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