Hmmm, this is my idea...

reversibility just implies that at any given moment in the transformation, the system and surroundings are in equilibrium, in which case, pressure is not constant. So, you would have to find an expression for pressure (based on isothermal compressibility coefficient, assumed to be unchanging throughout the transformation) and integrate over the change in volume (based on on coefficient of thermal expansion, also assumed to be unchanging throughout transformation). Presumably, for a solid, the amount of work in this case would be small.