A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P₀, volume V₀ and temperature T₀. If the gas mixture is adiabatically compressed to a volume V₀/4, then the correct statement(s) is/are, (Give $2^{1.2}$ = 2.3 ; $2^{3.2}$ = 9.2; R is gas constant)
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Question

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P₀, volume V₀ and temperature T₀. If the gas mixture is adiabatically compressed to a volume V₀/4, then the correct statement(s) is/are, (Give $2^{1.2}$ = 2.3 ; $2^{3.2}$ = 9.2; R is gas constant)

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G1 Physics · Accepted Answer

Use PV=nRT, U=(f/2)nRT, γ=1+2/f and vᵣₘₛ=√(3RT/M). At the same temperature, average translational kinetic energy depends only on T. Evaluating the given data/statements gives A: The final pressure of the gas mixture after compression is in between 9P₀ and 10P₀; C: The work |W| done during the process is 13RT₀; D: Adiabatic constant of the gas mixture is 1.6. Therefore the correct answer is A, C, D.