During this process the temperature is kept constant. Since the internal energy of ideal gases only depends on temperature: \(\Delta U=0\) and \(\Delta H=0\).
The first principle tells us: \(\Delta U=q+w\;\;\rightarrow q=-w\) . In this process, the heat exchanged is equal to the work done. We calculate the work done by the gas using the equation of state.
![](/images/termodinamica/primer-principio/gases-ideales-primer-principio/gases-ideales-primer-principio-31.png)
It can be put as a function of the initial and final state pressures using Boyle's law,
![](/images/termodinamica/primer-principio/gases-ideales-primer-principio/gases-ideales-primer-principio-32.png)
Substituting:
![](/images/termodinamica/primer-principio/gases-ideales-primer-principio/gases-ideales-primer-principio-33.png)