What is Isothermal Process?

For an ideal gas, $\Delta U$ depends only on temperature, so $\Delta U = 0$ and the heat absorbed equals the work done by the gas, $Q = W$. The pressure and volume obey $PV = \text{constant}$ (Boyle's law). To keep the temperature steady, the process must be slow and the gas must be in contact with a heat reservoir. In isothermal compression, the work is done on the gas and the same amount of heat flows out.