Question
A gas undergoes change from state $$A$$ to state $$B.$$ In this process, the heat absorbed and work done by the gas is $$5\,J$$ and $$8\,J,$$ respectively. Now gas is brought back to $$A$$ by another process during which $$3\,J$$ of heat is evolved. In this reverse process of $$B$$ to $$A$$ :
A.
$$10\,J$$ of the work will be done by the gas.
B.
$$6\,J$$ of the work will be done by the gas.
C.
$$10\,J$$ of the work will be done by the surrounding on gas.
D.
$$6\,J$$ of the work will be done by the surrounding on gas.
Answer :
$$6\,J$$ of the work will be done by the surrounding on gas.
Solution :
$$\eqalign{ & \Delta {U_{AB}} = q + w = + 5 + \left( { - 8} \right) = - 3 \cr & q = - 3,\,\Delta {U_{BA}} = + 3 \cr & \,\Delta {U_{BA}} = q + w \cr & \Rightarrow 3 = - 3 + w \Rightarrow w = + 6\,J\,{\text{(work done on the system)}}{\text{.}} \cr} $$
$$\eqalign{ & \Delta {U_{AB}} = q + w = + 5 + \left( { - 8} \right) = - 3 \cr & q = - 3,\,\Delta {U_{BA}} = + 3 \cr & \,\Delta {U_{BA}} = q + w \cr & \Rightarrow 3 = - 3 + w \Rightarrow w = + 6\,J\,{\text{(work done on the system)}}{\text{.}} \cr} $$