A steel tank filled with water has a volume of 1000 ft3. Near room temperature, the specific heat for water is c = 25.000 ft-lb/slug-oF, and its mass density is ( = 1.94 slug/ft3.
a. Compute the thermal capacitance C1 of the water in the tank.
b. Denote the total thermal resistance (convective and conductive) of the tank's steel wall by R1. The temperature of the air surrounding the tank is To. The tank's water temperature is T1. Assume that the thermal capacitance of the steel wall is negligible. Derive the differential equation model for the water's temperature, with T0 as the input.