In an Isothermal Process, the temperature ($T$) of the system remains constant.

1. Internal Energy: For an ideal gas, $U$ depends only on Temperature ($U=f(T)$). Therefore, $\Delta U=n{C}_v\Delta T=0$.
2. First Law: $\Delta U=q-w$ (with work done by system conventionally $w$).

• $0=q-w⟹q=w$.
• During isothermal expansion, the system absorbs heat ($q$) from the surroundings and converts it entirely into work ($w$) to keep the internal energy (and thus temperature) constant.