I understand that an isothermal process occurs at constant Temperature. And for an ideal gas, the the internal energy is a function of temperature only. Therefore, when Temp = 0, then U = 0 also, meaning the internal energy of the gas doesn't change... and we have q = - w or basically q = PΔV. All of the heat added to the system is used to do work. However, I read that Temperature = internal energy/ volume. When the gas does work, the volume increases. But if the volume decreases, it would affect the above equation and thusly would affect the temperature, so then how is the temperature constant? thanks!