If a gas absorbs heat, then how can its temperature remain constant? My book has this line:


  In an isothermal expansion, the gas absorbs heat and does work


But, if a gas absorbs heat, then how can its temperature remain constant? (as the process is isothermal)
From the first law, $\Delta U=Q-W$.  If the process is isothermal, then $\Delta U=0$ (assuming an ideal gas), so Q = W.  The heat energy is consumed by your gas doing work, so there is no change in internal energy (temperature).