A cyclic process for 1 , text{mol} of an idea | vedclass

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(C) For $1 \, 	ext{mol}$ of an ideal gas,the work done is given by $W = \int P \, dV$.$1$. Process $AB$: The volume $V$ is constant $(V = V_1)$. This

Vedclass · Accepted Answer

$0, R{T_2}\ln \left( {\frac{{{V_2}}}{{{V_1}}}} \right), R({T_1} - {T_2})$

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(C) For $1 \, 	ext{mol}$ of an ideal gas,the work done is given by $W = \int P \, dV$.$1$. Process $AB$: The volume $V$ is constant $(V = V_1)$. This is an isochoric process.Work done $W_{AB} = P \Delta V = 0$.$2$. Process $BC$: The temperature $T$ is constant $(T = T_2)$. This is an isothermal process.Work done $W_{BC} = \int_{V_1}^{V_2} P \, dV = \int_{V_1}^{V_2} \frac{RT_2}{V} \, dV = RT_2 \ln \left( \frac{V_2}{V_1} ight)$.$3$. Process $CA$: This is a process where the graph is a straight line passing through the origin in the $V-T$ diagram,implying $V \propto T$,which is an isobaric process.Work done $W_{CA} = P \Delta V = R \Delta T = R(T_1 - T_2)$.

$A$ cyclic process for $1 \, \text{mol}$ of an ideal gas is shown in the $V-T$ diagram. Find the work done in processes $AB$,$BC$,and $CA$ respectively.

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