Three moles of an ideal gas at 2 7 ∘ C are expanded isothermally to four times the volume and then heated at constant volume until the pressure returns to its initial value. The total heat supplied is

Question

Three moles of an ideal gas at 2 7 ∘ C are expanded isothermally to four times the volume and then heated at constant volume until the pressure returns to its initial value. The total heat supplied is 66.5 kJ. Find C v ​ C p ​ ​ (two decimals).

TestHub · Accepted Answer

Q 1 ​ = n RT ln 4 = 10.37 kJ. At constant volume the pressure returns to its initial value, so T rises from 300 K to 1200 K. Q 2 ​ = 66.5 − 10.37 = n C v ​ × 900 gives C v ​ = 20.79 J mol − 1 K − 1 = 2.5 R . γ = 1 + C v ​ R ​ = 1.40 , a diatomic gas.

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