Click and Clack, the tappet brothers, and their lawyers, Dewey, Cheatem, and How

Question

Click and Clack, the tappet brothers, and their lawyers, Dewey, Cheatem, and Howe, have been given the opportunity to invest in two proposed new inventions operating in cycles, which are decribed below. As there is alot of money involved if they decide to back these inventions, you must give a full asseeement of them, including your detailed reasoning.

a.) An inventor claims to have a cycle which has a heat input of 740 kW at a temperature of 800 degrees Celcius and a heat output of 202 kW at a temperature of 120 degrees Celcius. There is a net work output of 538 kW.

b.) The inventor's second cycle has a power input of 0.34 Horsepower. It has a heat input of 925.7 Btu/hr from a 10 degrees Farenheit source and produces heat output of 1791.0 Btu/hr to a 140 degrees Farenheit sink. ( 1 HP= 2545 Btu/hr)

Explanation / Answer

a) this type of cycle is impossible (heat engine) maximum efficiency is given by carnot cycle=( 1- (Tambient/T high temp)) * Q input. T amb=300k T high=800+273=1073.from this we get maximum output can be 534 w.but it is claimed 538 at 393 k which is impossible b)this is possible.similar to heat pump. work input=0.34*2545=865.3,Q lower=925.7. Q output = Q input + work input= 925.7+865.3= 1791. same as they claimed.no thermodynamic law is violated.so invest in this

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