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(D) According to the first law of thermodynamics,the heat energy $\Delta Q$ given to the system is given by $\Delta Q = \Delta U + \Delta W$.Since int

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path $AFB$

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(D) According to the first law of thermodynamics,the heat energy $\Delta Q$ given to the system is given by $\Delta Q = \Delta U + \Delta W$.Since internal energy $U$ is a state function,the change in internal energy $\Delta U$ is the same for all paths from state $A$ to state $B$.Therefore,the heat energy $\Delta Q$ is minimum when the work done $\Delta W$ by the system is minimum.The work done $\Delta W$ in a $P-V$ diagram is equal to the area under the curve.Comparing the areas under the paths $ACB$,$ADB$,$AEB$,and $AFB$,the area under the path $AFB$ is the smallest.Thus,the work done is minimum for path $AFB$,and consequently,the energy given to the system is minimum in path $AFB$.

An ideal system can be brought from state $A$ to $B$ through four paths as shown in the figure. The energy given to the system is minimum in

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