In a thermodynamic process, 2 , text{moles} o | vedclass

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(B) The given process is a polytropic process defined by $P \propto V^{-2}$, which can be written as $P V^2 = 	ext{constant}$.Comparing this with the

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$-200$

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(B) The given process is a polytropic process defined by $P \propto V^{-2}$, which can be written as $P V^2 = 	ext{constant}$.Comparing this with the general polytropic equation $P V^n = 	ext{constant}$, we get the polytropic index $n = 2$.The work done by an ideal gas in a polytropic process is given by the formula $W = \frac{\mu R (T_1 - T_2)}{n - 1}$, or equivalently $W = \frac{\mu R \Delta T}{1 - n}$.Given: number of moles $\mu = 2$, initial temperature $T_1 = 300 \, K$, final temperature $T_2 = 400 \, K$, and $n = 2$.Substituting these values into the formula:$W = \frac{2 	imes R 	imes (400 - 300)}{1 - 2}$$W = \frac{2 	imes R 	imes 100}{-1}$$W = -200 \, R$.Thus, the work done by the gas is $-200 \, R$.

In a thermodynamic process, $2 \, \text{moles}$ of a monatomic ideal gas obey $P \propto V^{-2}$. If the temperature of the gas increases from $300 \, K$ to $400 \, K$, find the work done by the gas in terms of $R$ (where $R$ is the universal gas constant).

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