If a system has 225 kcal of work done to it, and releases 5.00 × 102 kj of heat into its surroundings, what is the change in internal energy of the system?

We can solve the problem by using the first law of thermodynamics:

where

is the change in internal energy of the system

is the heat absorbed by the system

is the work done by the system on the surrounding

In this problem, the work done by the system is

with a negative sign because the work is done by the surrounding on the system, while the heat absorbed is

with a negative sign as well because it is released by the system.

Therefore, by using the initial equation, we find