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(A) According to the first law of thermodynamics,the change in internal energy $\Delta U$ is a state function and depends only on the initial and fina

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$20$

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(A) According to the first law of thermodynamics,the change in internal energy $\Delta U$ is a state function and depends only on the initial and final states,not on the path taken.For both paths $abc$ and $adc$,the initial state is $a$ and the final state is $c$,so $\Delta U$ remains the same.For path $abc$:$\Delta U = Q_{abc} - W_{abc} = 80 \ cal - 35 \ cal = 45 \ cal$.For path $adc$:Since $\Delta U$ is the same,$\Delta U = 45 \ cal$.Given $Q_{adc} = 65 \ cal$,we use the first law of thermodynamics again:$\Delta U = Q_{adc} - W_{adc}$$45 \ cal = 65 \ cal - W_{adc}$$W_{adc} = 65 \ cal - 45 \ cal = 20 \ cal$.

When a system is taken from state $a$ to state $c$ along a path $abc$,it is found that $Q = 80 \ cal$ and $W = 35 \ cal$. Along path $adc$,$Q = 65 \ cal$. The work done $W$ along path $adc$ is: (in $cal$)

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