I need help with this thermodynamics homework problem Thank u A new die-casting

Question

I need help with this thermodynamics homework problem

Thank u

A new die-casting operation has a large amount of waste heat available at 200 degree C m a location where the local environmental temperature is 20.0degree. As chief engineer in Charge of thermal energy management investigate the possibility of recovering some of this waste heat by determining (a.) the thermal efficiency of a Carnot engine operating between these temperatures. (b.) The coefficient of performance of a Carnot heat pump operating between these temperatures.

Explanation / Answer

T1 = 20 deg = 293 K

T2 =200 deg = 473 K

a)

Thermal efficiency = 1-T1/T2 = 1- 293/473 = 0.381

Thermal efficiency =38.1%

b)

COP of a heat Pump = T2/(T2-T1) = 473/(473-293) = 2.628

c)

COP of a refrigerator = T1/(T2-T1) = 1.628

d)

T1 = 273 K

T2 = 473 K

Thermal efficiency = 1-T1/T2 = 1- 273/473 = 0.423

Thermal efficiency =42.3%

COP of a heat Pump = T2/(T2-T1) = 473/(473-273) = 2.365

COP of a refrigerator = T1/(T2-T1) = 1.365

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