When heat is supplied to a diatomic gas, the external work done by the gas is $\frac{1}{3}$ of change of internal energy. The molar specific heat of the gas is

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1.4R

10R

3.33R

answer is B.

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Detailed Solution

$here dW = \frac{dU}{3} from 1 st law of thermodynamics dQ = dU + dW = dU + \frac{dU}{3} = \frac{4}{3} dU but dU = {nC}_{v} dT = n \frac{5 R}{2} dT dQ = \frac{4}{3} n \frac{5 R}{2} dT molar specific heat = \frac{dQ}{ndT} = \frac{10 R}{3}$

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