I am having trouble understanding why in an isothermal process, the change in internal energy is zero. I know that $\Delta U$ or $\Delta E=q+w$, and so in isothermal process $q=0$. But how does one show that $w =0$? Or is it necessary that if we are talking of isothermal process, we are not doing work on the system; why or why not? Or is it necessary that if $w$ is not equal to 0, then the process can't be isothermal; why? Please explain this. I found a similar question here but I was not able to understand anything from it.