Question

A reversible engine is supplied with heat from two constant temperature sources at 800K and 400K and rejects heat to a constant temperature sink at 300K. The engine develops work equivalent to 80kJ/s and rejects heat at the rate of 46kJ/s. Deduce: i. Heat supplied by each source. [5] ii. Thermal efficiency of the engine. [5]

Answer 1

Answer:

Given dataT1=750K,T2=500K,T3=250K,Wengine=100kw, Q′1=3600KJ⁄min=60KW

Q1+Q2=W+Qr from the problem

Q1+Q2=100+60………(1)

η1=T1−T3T1 =750−250750=.66,

η2=T2−T3T3 =500−250500=0.5

W1=η1Q1=0.66Q1

W1=η1Q1=0.5Q2

total work(W)=W1+W2=0.66Q1+0.5Q2

100=0.66Q1+0.5Q2………(2)

Solving eq 1 and eq 2 we get values of Q1 and Q2

Q1=119.76KW , Q2=40.239KW

Efficiency of the engine (η):

=totalworkdone(totalheatabsorbs=100160=62.5%

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