A monoatomic 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:

The work done on the gas is $$W = -P \cdot \Delta V$$

$$W = -100 \cdot (1 - 2) = 100 \text{ J}$$

This 100 J represents energy transferred into the gas through mechanical work.

In the second step, the gas is heated at a constant volume. 

Energy supplied ($$Q$$) = 150 J. Work done ($$W$$) = 0 J (since volume does not change)

$$\Delta U_2 = 150 \text{ J}$$

$$\Delta U_{total} = \text{Work done on gas} + \text{Heat supplied}$$

$$\Delta U_{total} = 100 \text{ J} + 150 \text{ J} = 250 \text{ J}$$