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(C) Internal energy for a thermodynamic process is a state function,meaning it does not depend upon the path taken; it only depends upon the initial a

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$Q_1-W_1=Q_2-W_2$

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(C) Internal energy for a thermodynamic process is a state function,meaning it does not depend upon the path taken; it only depends upon the initial and final states of the system.Therefore,if two different processes have the same initial and final states,the change in internal energy $\Delta U$ will be the same for both processes.According to the first law of thermodynamics: $Q = W + \Delta U$,which can be rearranged as $\Delta U = Q - W$.For path $1$: $\Delta U = Q_1 - W_1$.For path $2$: $\Delta U = Q_2 - W_2$.Since $\Delta U$ is the same for both paths,we have: $Q_1 - W_1 = Q_2 - W_2$.

$A$ system is taken from state $A$ to state $B$ along two different paths. The heat absorbed and work done by the system along these two paths are $Q_1, Q_2$ and $W_1, W_2$ respectively,then

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