Four moles of a certain ideal gas at 3 0 ∘ C are expanded isothermally to three times the volume and then heated at this constant volume until the pressure is raised to its initial value. In the whole

Question

Four moles of a certain ideal gas at 3 0 ∘ C are expanded isothermally to three times the volume and then heated at this constant volume until the pressure is raised to its initial value. In the whole process the heat supplied is 72 kJ. Calculate the ratio C v ​ C p ​ ​ for the gas and state whether it is monoatomic, diatomic or polyatomic.

TestHub · Accepted Answer

Q 1 ​ = n RT ln 3 = 4 × 8.314 × 303 × 1.0986 = 11.07 kJ. At constant volume the pressure returns to its initial value, so the temperature triples: Δ T = 606 K. Q 2 ​ = 72 − 11.07 = 60.93 kJ = 4 C v ​ × 606 , so C v ​ = 25.1 J mol − 1 K − 1 = 3.02 R . γ = 1 + C v ​ R ​ = 1.33 , a polyatomic gas.

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