3 Kg mass of water is heated to atemperature of 99.5 C at 1 bar of pressure. It is slowly pouredinto a heavily insulated beaker containing 7.5 Kg of water at atemperature and pressure of 4 C, 1 bar, respectively. The specificheat of the water, an incompressible material is, c = 4.1 KJ/(KgK). The beaker can be considered to be an adiabatic system. The twowater mass’ reach an equilibrium temperature. There is no kineticor potential change in this problem. The dead state pressure isdefined as Po = 1 bar. Instead of mixing the two fluidstogether consider the following proposal. Heat is allowed to flowfrom the 3 Kg mass of water through a Carnot heat engine and isrejected to the surroundings. Determine the maximum amount of workthat could be performed, and the exergy destroyed during theoperation.
In this case the temperature and internal energy of the mass ofwater is changing unlike the infinite heat reservoir case.Since thetemperature of the high temperature heat input is changing theCarnot efficiency is also changing.In order to account for thischange, you should consider using an energy balance for every 5 Cchange in the temperature of the 3Kg water mass and calculate theCarnot efficiency at the average temperature.For example, in thefirst numerical step the temperature of the water mass would changefrom 99.5 to 94.5 C and the Carnot efficiency for this temperaturestep would be T = 370 K.You should determine the incremental workdone during this step with an energy balance on the heat engine.The exergy destruction is calculated in a similar incrementalmanner.
(a) Calculate the work output and entropy production when the 3Kg mass of water is brought into equilibrium with surroundings at 4C.
(b)Compare the exergy destroyed between the mixing process andthe heat engine process.
