# A system is taken from state A to state B along two different paths 1 and 2. The Work done on the system along these two path is $W_1$ and $W_2$ The heat absorbed by the system along these paths are $Q_1$ and $Q_2$ respectively. Then

$(a)\;Q_1=Q_2 \\(b)\; W_1+Q_1=Q_2+W_2 \\(c)\;W_1=W_2 \\(d)\;Q_1-W_1=Q_2-W_2$

By first law of thermodynamics
$Q_1+(-W_1) = Q_2+ (-W_2)$
Hence $Q_1-W_1=Q_2-W_2$ is correct.
Hence d is the correct answer.
edited Mar 6