A gas sample in a piston assembly expands, doing 564 kJ of work on its surroundings at the same time that 344 kJ heat is added to the gas. What is the change in internal energy of the gas during this process?

Here we have to get the change of internal energy by the gas due to the 564 kJ work done by the system and addition of 344 kJ heat to the system.

The change of internal energy of the gas during this process is (+) 908 kJ

We know the summation of heat capacity (ΔU) and work done by a system is equivalent to the heat energy (ΔH).

Or, mathematically we may write, ΔU + W = ΔH.

Now the work done by the system (W) is (-) 564 kJ. The negative sign implies the work done by the system to surroundings as per thermodynamics.

The heat added to the gas (ΔH) is (+) 344 kJ. The positive sign indicate the addition of heat to the system.

On plugging the values: ΔU + (-) 564 kJ = (+) 344 kJ

Or, ΔU - 564 kJ = 344 kJ

Or, ΔU = 344 kJ + 564 kJ

Thus the change of internal energy, ΔU = (+) 908 kJ.