One mole of an ideal monoatomic gas at temper | vedclass

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(A) For a polytropic process $P V^x = 	ext{constant}$, the molar heat capacity $C$ is given by $C = C_V + \frac{R}{1-x}$.Given the process law is $P/

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$2 R T_0$

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(A) For a polytropic process $P V^x = 	ext{constant}$, the molar heat capacity $C$ is given by $C = C_V + \frac{R}{1-x}$.Given the process law is $P/V = 	ext{constant}$, we can write it as $P V^{-1} = 	ext{constant}$.Thus, the polytropic index $x = -1$.For an ideal monoatomic gas, the molar heat capacity at constant volume is $C_V = \frac{3}{2} R$.Substituting these values, $C = \frac{3}{2} R + \frac{R}{1-(-1)} = \frac{3}{2} R + \frac{R}{2} = 2 R$.The heat supplied is given by $\Delta Q = n C \Delta T$.Given $n = 1$ mole and $\Delta T = 2 T_0 - T_0 = T_0$.Therefore, $\Delta Q = 1 	imes (2 R) 	imes T_0 = 2 R T_0$.

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P/V = \text{constant}$. If the final temperature is $2 T_0$, heat supplied to the gas is:

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