When the state of a gas adiabatically changed from an equilibrium state $$A$$ to another equilibrium state $$B$$ an amount of work done on the stystem is $$35\,J.$$  If the gas is taken from state $$A$$ to $$B$$ via process in which the net heat absorbed by the system is $$12\,cal,$$  then the net work done by the system is
$$\left( {1\,cal = 4.19\,J} \right)$$

Solution :
In the first-case adiabatic change,
$$\Delta Q = 0,\Delta W = - 35\,J$$
From $${1^{st}}$$  law of thermodynamics,
$$\eqalign{ & \Delta Q = \Delta U + \Delta W, \cr & {\text{or}}\,\,0 = \Delta U - 35 \cr & \therefore \Delta U = 35\,J \cr} $$
In the second case
$$\eqalign{ & \Delta Q = 12cal = 12 \times 4.2\;J = 50.4\,J \cr & \Delta W = \Delta Q - \Delta U = 50.4 - 35 = 15.4\,J \cr} $$