Question

3 Kg mass of water is heated to a temperature of 99.5 C at 1 bar of pressure. It is slowly poured into a heavily insulated beaker containing 7.5 Kg of water at a temperature and pressure of 4 C, 1 bar, respectively. The specific heat of the water, an incompressible material is, c = 4.1 KJ/(Kg K). The beaker can be considered to be an adiabatic system. The two water mass’ reach an equilibrium temperature. There is no kinetic or potential change in this problem. The dead state pressure is defined as P_o = 1 bar. Instead of mixing the two fluids together consider the following proposal. Heat is allowed to flow from the 3 Kg mass of water through a Carnot heat engine and is rejected to the surroundings. Determine the maximum amount of work that could be performed, and the exergy destroyed during the operation.

In this case the temperature and internal energy of the mass of water is changing unlike the infinite heat reservoir case.Since the temperature of the high temperature heat input is changing the Carnot efficiency is also changing.In order to account for this change, you should consider using an energy balance for every 5 C change in the temperature of the 3Kg water mass and calculate the Carnot efficiency at the average temperature.For example, in the first numerical step the temperature of the water mass would change from 99.5 to 94.5 C and the Carnot efficiency for this temperature step would be T = 370 K.You should determine the incremental work done during this step with an energy balance on the heat engine. The exergy destruction is calculated in a similar incremental manner.

(a) Calculate the work output and entropy production when the 3 Kg mass of water is brought into equilibrium with surroundings at 4 C.

(b)Compare the exergy destroyed between the mixing process and the heat engine process.

Answer 1