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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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$6$

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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 the path $iaf$:$Q_{iaf} = \Delta U + W_{iaf}$$50 \ cal = \Delta U + 20 \ cal$$\Delta U = 50 - 20 = 30 \ cal$Since the initial state $i$ and final state $f$ are the same for path $ibf$,the change in internal energy $\Delta U$ remains the same.For the path $ibf$:$Q_{ibf} = \Delta U + W_{ibf}$$36 \ cal = 30 \ cal + W_{ibf}$$W_{ibf} = 36 - 30 = 6 \ cal$

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