This is an oversimplification of a practical problem I am currently trying to design for. Suppose, we have a very long cylinder closed at both ends which contains water at a given pressure P1 and temperature T1. P1 and T1 are such that water is in a compressed state (subcooled). One end of the vessel is heated slowly. The cylinder is sufficiently long so that there is temperature gradient within the volume of water inside the cylinder. As one can imagine the pressure of water increases. 1. How to determine the increase in pressure? Additionally, a relief valve is provided. The valve opens to relieve pressure once the pressure reaches P2. 2. How much volume will need to be vented to relieve the built up pressure?