Click and Clack the tappet brothers and their lawyers Dewey

Click and Clack, the tappet brothers, and their lawyers, Dewey, Cheatem, and Howe, have been given the \"fabulous opportunity\" to invest in two proposed new inventions operating in cycles, which are described below. As there is a lot of money involved if they are decide to back these inventions, you must give a full thermodynamic assessment of them including your detailed reasoning. An inventor claims to have a cycle which has heat input at 120 degree C output at 825 degree C. The input rate is 505 kW and the output rate is 1850 kW. There is a net work input power of 1345 kW. The inventor\'s second cycle has a net power output of 6.80 HP. It has a heat input rate of 35820 Btu/hr from a 440 degree F source and procedures heat output of 18514 Btu/hr to a 10 degree F sink. [1 HP = 2545 Btu/hr]

Solution

a.

For the given cycle with heat input of 505kW at 393K, heat rejection of 1850kW with 1098K with heat input of 1345kW

Carnot COP = T_L(T_H-T_L) = 393/(1098-393) = 0.557

From energy values, actual COP = Qinput/(W_input) = 505/1345 = 0.3754

actual COP < carnot COP so cycle is possible

b.

the cycle has power output of 17306 Btu/hr with heat supply of 35820 Btu/hr at 499.817 K and heat rejection of 18514 Btu/hr at 260.928 K.

carnout Efficiency = 1-(T_L/T_H) = 1-(260.928/499.817) = 0.47795

from energy values actual Efficiency = W_net/H_input = 17360/35820 = 0.4846

actual efficieny is greater than carnout efficiency so cycle is not possible in reality.