Question

1. A Carnot heat engine works between 450^oC and 25^oC. The work output is used to drive a Carnot refrigerator that removes heat from -15^oC space at a rate of 400kJ/min and rejects the heat to 25 ^oC environment.

1. Find the rate of heat supplied to the heat engine
2. Find the total rate of heat rejection to the environment

ii) In the steady state of a steam turbine operation, steam enters a turbine at a rate of 25000 kg/hr at 4MPa and 550^oC. The steam expands and leaves the turbine as saturated vapor at 50kPa. The power produced by the turbine is 6MW.

1. Given the surrounding is at 25^oC, find the rate of entropy generation.

b. The turbine has an isentropic efficiency of 90%. Find the power output of the turbine.

Answer 1

The Combination of Heat Engine and Refrigrator is shown in the Diagram Above

29 0 fQ3 = 400 kJ/mui

$COP=\frac{Q3}{Q4-Q3}$$COP=\frac{258}{298-258}=\frac{400}{Net Work}$

Net Work = 62.01 KJ/Min

$Efficiency of Engine =\frac{Net Work}{Qsupplied}$$Efficiency of Engine =\frac{723-523}{723}=\frac{62.01}{Qsupply}$Qsupply= 224.186 KJ/min

Heat Rejected = 62.01 + 400

Heat Rejected = 462.015 KJ/min