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(A) For a monatomic ideal gas, the molar heat capacity $C$ for a polytropic process $PV^x = 	ext{constant}$ is given by $C = C_V + \frac{R}{1-x}$.Giv

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$4 R / 2$

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(A) For a monatomic ideal gas, the molar heat capacity $C$ for a polytropic process $PV^x = 	ext{constant}$ is given by $C = C_V + \frac{R}{1-x}$.Given the process is $P/V = 1$, which implies $P = V^1$, or $PV^{-1} = 	ext{constant}$.Comparing this with $PV^x = 	ext{constant}$, we get $x = -1$.For a monatomic gas, the molar heat capacity at constant volume is $C_V = \frac{3R}{2}$.Substituting the values into the formula: $C = \frac{3R}{2} + \frac{R}{1 - (-1)}$.$C = \frac{3R}{2} + \frac{R}{2} = \frac{4R}{2} = 2R$.

$A$ monatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals to $1$. What is the molar heat capacity of the gas?

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