Question

You want a company to build a thermal power plant in your neighborhood in order to supply electrical power. Concerned with environmental procedure, it is required that the efficiency of the plant’s system would be at least 70% . You got a call from a company that said they could meet this efficiency. They claim that they could burn their coal in a way such that the hot reservoir for their heat engine is maintained at 626 degrees Celsius. You have also learned from local environmental scientists that the river running next to the power plant has an average temperature of 21 degrees Celsius, which would act as the cold reservoir for the power plant. The hot and cold reservoirs are respectively the heat supplier and the heat dump for a heat engine that performs mechanical work. The power plant’s system then converts this mechanical work into electric energy.

Draw the PV diagram for a singular heat cycle of the mechanical heat engine. Assume that it is a Carnot Engine that starts off from an initial state 1; next, it expands isothermally to another state 2, whereafter it cools adiabatically to state 3; it then compresses isothermally to state 4; and lastly, its temperature rises adiabatically such that its state returns to the original state 1. Clearly label each state, and the parts of the cycle as adiabatic/isothermal. Once again assuming that the heat engine is a Carnot Engine, determine whether it is possible that the company’s power plant could meet the required efficiency (Assume that all of the mechanical work is turned into electrical energy).

Answer 1