Question

An inventor claims to have developed a power cycle operating between hot and cold reservoirs at 1350 K and 295 K, respectively, that provides a steady-state power output of (a) 30.00 kW, (b) 33.33 kW, while receiving energy by heat transfer from the hot reservoir at the rate 150,000 kJ/h. Evaluate each claim.

Answer 1

efficiency = 0.71999 < 0.78148

efficiency = 0.7999 ≈ 0.78148

Step-by-step explanation:

given data

Hot reservoir Temp Th = 1350 K

Cold reservoir Temp Tc = 295 K

heat transfer rate = 150,000 kJ/h

solution

first we get here maximum possible efficiency that is express as

maximum possible efficiency = 1 -
`(Tc)/(Th)` ..........1

put here value and we get

maximum possible efficiency = 1 -
`(295)/(1350)`

maximum possible efficiency = 0.78148

and

efficiency =
`(Wout)/(Qin)` .................2

here Qin =
`(150000)/(3600)` = 41.667

so put here value in equation 2 we get

efficiency =
`(30)/(41.667)`

efficiency = 0.71999 < 0.78148

and

efficiency =
`(33.33)/(41.667)`

efficiency = 0.7999 ≈ 0.78148

claim might be true or not because there always be looser