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Question

An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation $$P =kV$$. Molar heat capacity of the gas for the process is 


A
C=CV+R
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B
C=CV+ R2
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C
C=CV R2
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D
C=CV+2R
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Solution

The correct option is A $$C=C_{V}+ \displaystyle\ \dfrac{R}{2}$$
$$P=kV \Rightarrow$$
$$PV^{-1} = k$$
It is polytropic process ($$PV^{n}= $$constant)
So $$n = -1$$
So, $$C = C_{V} + \displaystyle\ \dfrac{R}{1-n} =  C_{V} + \displaystyle\ \dfrac{R}{2}$$

Physics

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