A sample of gas in a cylinder is provided with 623.9 kJ of heat. This causes a piston to then compresses the gas by doing 432.9 kJ of work to the gas. What is the change in internal energy of the gas during this compression?

1056.8 kJ

Explanation:

A sample of gas in a cylinder is provided with 623.9 kJ of heat. By convention, when the gas absorbs heat, it takes a positive sign, so Q = 623.9 kJ.

A piston then compresses the gas by doing 432.9 kJ of work to the gas. We work is done on the gas, it takes a positive sign, so W = 432.9 kJ.

The change in the internal energy (ΔU) is:

ΔU = Q + W

ΔU = 623.9 kJ + 432.9 kJ = 1056.8 kJ