Question

21 A Carnot heat engine receives heat from a reservoir at 700°C at a rate of 6 MW and rejects the waste heat to the ambient at 300 K, as shown in the figure. The entire net power output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cold medium at -10°C and transfers it to the same ambient at 300 K. Determine:35235333333 a) The thermal efficiency of the heat engine. b) The COP of the refrigerator. 135 c) The rate of heat removed from to the cold medium in kW. d) The total rate of heat rejection to the ambient in kW. (700°C Tom # (-10°C la B < Ambient, 300 K

Answer 1

• carnot cycle is the ideal cycle and given question can be solved by equations of ideal carnot cycle
• The entire work output of the engine is given as work input to the refrigerator

a) thermal efficiency of heat 6 criven Data | -) For Heat Engine • Reservoir temperature (71) Ti 700°C = 973k Ambient temperature (Tz) T2 = 844 300k • Heat input (ainz - 2; z 6MW 2) For Refaigerator • Reforgesation temperature (ti) tiz-10°c = 263k • Ambient temperature (tz) tzz 3ook a) For carnst heat engine olazi-Qi engine na t o El-184 R = 0.693= 69.37) • Now, w for refrigerator z G15 MW - Wz Qur- QLIR - (1) • also, for carnst Rofrigerator ti z QLIR t₂-ti 263 300-263 6.15 Il z Qi 4 /5 QL, R2 29.49 MW from equation ci) - 4.15 2 QAR - QLIR 24, R = 33.64 MW b) cop of Refrigerator COPRE Q R 2 22.49 27-1 W COPRE 7-11 c) Rate of heat removed foom cold mediam Q1,R2 29:49x10kw d) total heat rejection to ambient Qot Q fyr = 1189x10'+ 33.64x102 235:48/109kW 300 o & 21.84 mW · hence, heat rejected by heat engine a. 1.84mW work outputz Qi-a. W-o z 6-1.84 w.o. 6.15MW