In a large steam power plant, the combustion of coal provides a heat rate of qin  = 2500 MW at a flame temperature of Th  = 1000 K. Heat is rejected from the plant to a river flowing at  Tc  = 300 K.  Heat  is  transferred  from  the  combustion  products  to  the  exterior  of large tubes in the boiler by way of radiation and convection, through the boiler tubes by conduc- tion,  and  then  from  the  interior  tube surface  to  the  working  fluid  (water)  by  convection. On the cold side, heat is extracted from the power plant by condensation of steam on the exterior condenser tube surfaces, through the condenser tube walls by conduction, and from the interior of the condenser tubes to the river water by convection. Hot and cold side ther- mal resistances account for the combined effects of conduction, convection, and radiation and,  under  design  conditions,  they  are  Rt,h  =  8 X 10-8  K/W  and  Rt,c  = 2 X 10-8  K/W, respectively.

1. Determine the efficiency and power output of the power plant, accounting for heat transfer effects to and from the cold and hot reservoirs. Treat the power plant as an internally reversible heat engine.

2. Over time, coal slag will accumulate on the combustion side of the boiler tubes. This fouling processincreases the hot side resistance to Rt,h  = 9 X 10-8  K/W. Concurrently, biological  matter  can  accumulate  on  the  river  water  side  of  the  condenser  tubes, increasing the cold side resistance to Rt,c  = 2.2 X 10-8  K/W. Find the efficiency and power output of the plant under fouled conditions.