Heat and Thermal ExpansionHard

Question

One mole of an  ideal gas ungderoes a whose molar heat capacity is 4R and in which work done by gas for small change in temperature is given by the relation dW = 2RdT, then the ration is.

Options

A.7/5
B.5/3
C.3/2
D.2

Solution

For small change dQ = dU + dW
nCdT = nCVdT + 2nRdT ∴ C = CV + 2R ; 4R = CV + 2R ∴ CV = 2R
Allso CV = = 2R ⇒ 2γ - 2 = 1 ⇒ γ = 32

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