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
