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

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$Q_A - W_A = Q_B - W_B = Q_C - W_C$

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(D) According to the first law of thermodynamics,$Q = \Delta U + W$,where $Q$ is the heat supplied to the system,$\Delta U$ is the change in internal energy,and $W$ is the work done by the system.Since internal energy is a state function,the change in internal energy $\Delta U = U_2 - U_1$ depends only on the initial state $1$ and the final state $2$. Therefore,$\Delta U$ is the same for all paths $A, B$,and $C$.From the first law,$Q - W = \Delta U$.Since $\Delta U$ is constant for all paths,the value of $(Q - W)$ must also be the same for all paths.Thus,$Q_A - W_A = Q_B - W_B = Q_C - W_C = \Delta U$.Therefore,the correct condition is $Q_A - W_A = Q_B - W_B = Q_C - W_C$.

The given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths $A, B, C$. Let $Q, W$,and $\Delta U$ represent the heat supplied to the gas,work done by the gas,and the change in internal energy of the gas,respectively. Which of the following conditions is true?

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