Thermodynamics of freezing water inside a self-pressurizing elastic tank and its departure from isochoric condition

Abstract

We present a mathematical model that considers the formation of an ice layer with expansion in a container with a moving boundary. The displacement represents the strain of the tank when the solidifying water expands. The results show that the ice and liquid fractions inside the tank depend on the spring constant and dimensions of the tank. If the spring constant tends to infinity, the ice and liquid fractions are those corresponding to an isochoric process. For each temperature, there is a threshold value of the spring constant, below which all the contents of the tank become ice and above which a smaller fraction does so. The threshold value of the spring constant relates to the degree to which water expands as it freezes. Structural design of a tank shows that the process departs from isochoric. Keeping the process completely isochoric requires oversizing the tank with corresponding increases in manufacturing costs and transportation weight.