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(A) According to the first law of thermodynamics,$\Delta Q = \Delta U + \Delta W$,where $\Delta Q$ is the heat supplied,$\Delta U$ is the change in in

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$900$

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(A) According to the first law of thermodynamics,$\Delta Q = \Delta U + \Delta W$,where $\Delta Q$ is the heat supplied,$\Delta U$ is the change in internal energy,and $\Delta W$ is the work done by the system.Since the initial state $P$ and final state $Q$ are the same for both paths,the change in internal energy $\Delta U$ is the same for both paths.For path $1$: $\Delta Q_1 = \Delta U + \Delta W_1 = 1000 \ J$.For path $2$: $\Delta Q_2 = \Delta U + \Delta W_2$.Given that $\Delta W_1 = \Delta W_2 + 100 \ J$,we can write $\Delta W_2 = \Delta W_1 - 100 \ J$.Substituting this into the equation for path $2$: $\Delta Q_2 = \Delta U + (\Delta W_1 - 100 \ J) = (\Delta U + \Delta W_1) - 100 \ J$.Since $\Delta U + \Delta W_1 = 1000 \ J$,we have $\Delta Q_2 = 1000 \ J - 100 \ J = 900 \ J$.

In the given $PV$ diagram,a system goes from state $P$ to state $Q$ along two different paths. Along path $1$,the system is given $1000 \ J$ of heat. The work done by the system along path $1$ is $100 \ J$ more than the work done along path $2$. How much heat is transferred along path $2$ (in $J$)?

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