A gas is compressed from a volume of $$2{m^3}$$  to a volume of $$1{m^3}$$  at a constant pressure of $$100\,N/{m^2}.$$   Then it is heated at constant volume by supplying $$150\,J$$  of energy. As a result, the internal energy of the gas:

Solution :
As we know,
$$\eqalign{ & \Delta Q = \Delta U + \Delta W\,\,\left( {{{\text{1}}^{{\text{st}}}}{\text{ law of thermodynamics}}} \right) \cr & \Rightarrow \Delta Q = \Delta U + P\Delta V \cr & {\text{or}}\,\,150 = \Delta U + 100\left( {1 - 2} \right) = \Delta U - 100 \cr & \therefore \Delta U = 150 + 100 = 250\,J \cr} $$
Thus the internal energy of the gas increases by $$250\,J$$