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(B) According to the first law of thermodynamics,$Q = \Delta U + W$,where $Q$ is the heat supplied,$\Delta U$ is the change in internal energy,and $W$

Vedclass · Accepted Answer

$W_A > W_B > W_C$

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(B) According to the first law of thermodynamics,$Q = \Delta U + W$,where $Q$ is the heat supplied,$\Delta U$ is the change in internal energy,and $W$ is the work done by the gas.Since internal energy $U$ is a state function,the change in internal energy $\Delta U = U_2 - U_1$ depends only on the initial state $1$ and final state $2$. Therefore,$\Delta U$ is the same for all three paths $A, B,$ and $C$.In a $P-V$ diagram,the work done $W$ by the gas is equal to the area under the curve. From the given diagram,the area under curve $A$ is the largest,followed by curve $B$,and then curve $C$. Thus,$W_A > W_B > W_C$.Since $\Delta U$ is constant for all paths,the heat supplied $Q = \Delta U + W$ will follow the same order as the work done: $Q_A > Q_B > Q_C$.Also,for any path,$Q - W = \Delta U$. Since $\Delta U$ is the same for all paths,$Q_A - W_A = Q_B - W_B = Q_C - W_C = \Delta U$. Therefore,option $B$ is the correct statement.

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