Compare the entropy and energy storage of a tank having a volume of 1.0 m^3 for two situations: (1) the tank is filled with water; (2) two thirds of the volume of the tank is taken up by an inset container filled with sodium suflate decahydrate (Na2SO4·10H2O) which is a phase change material (PCM), the rest of the volume is occupied by water. (The container is surrounded by the water.)
Properties of sodium suflate decahydrate:
c_p_solid / J/(K·kg) | 1920 | c_p_liquid / J/(K·kg) | 3260 | k_E_solid / W/(K·m) | 0.514 | k_E_solid / W/(K·m) | 0.475 | Tf (temp of fusion) / K | 32+273 | q (enthalpy of fusion) / J/kg | 2.51·10^5 | rho_solid / kg/m^3 | 1460 | rho_liquid / kg/m^3 | 1330 |
a. For Case (1), how much entropy and energy can be stored in the tank if the temperature of the water rises from 25°C to 40°C? b. For Case (2), how much entropy and energy can be stored in the tank if the temperature of the water and of the PCM rise from 25°C to 40°C? | | c. Assuming that the temperature coefficients of enthalpy (c_p) of water and of the PCM are constant, what are the specific entropy capacitances of these two materials? d. Produce a table representing the T-s relation (temperature - specific entropy) for the PCM. Set the entropy of the PCM equal to zero at 0°C. e. Create a dynamical model for the temperature of the materials in the tank for the following situation. The tank is perfectly insulated. The water in the tank is heated with an immersion heater having a specified electric power. Use a single storage element in the model for the water. Use a single storage element for the PCM in its container. f. The answers to questions a and b show that more entropy can be stored in the tank having the PCM. Consider the tank without insulation sitting in a room being used to heat the room. Is there another advantage (than the fact that more entropy can be stored) to using the tank with PCM for heating the room? g. The tank is charged with warm water from a hot water solar collector. Could the fact that entropy has to be conducted through the PCM to make it hotter and let it melt be a disadvantage in using a warm water tank with PCM? (Note that the water in the tank is circulated through the collector.) In other words, could there be a problem with the dynamics of warming and melting of the solid PCM? |
