Question

a carnot heat engine delivers 500 kj of heat per cycle to a hightemperature source at 652 oc and receives heat from a low-temperature sink at 30 oc. determine: a) the efficiency of this carnot engine b) the amount of heat rejected to the sink per cycle

Answer 1

a) The efficiency of this carnot engine = 0.672 = 67.2%

Carnot heat engine converts 67.2% of the heat it receives to work.

b) The amount of heat rejected to the sink per cycle = 164 kJ

$Q_{H}$ = 500 kJ

Efficiency of this carnot engine =?

Amount of heat rejected to the sink per cycle =?

a) Carnot heat engine is a reversible heat engine; its efficiency can be calculated from:

$n_{th,rev} = 1 - \frac{T_{L} }{T_{H} }$

$n_{th,rev} = 1 - \frac{(30+273)K}{(652+273)K}$

= 0.672

The efficiency of this carnot engine = 0.672 = 67.2%

b) The amount of heat rejected $Q_{L}$ by heat reversible engine can be calculated from:

​$(\frac{Q_{H} }{Q_{L} } )_{rev} = \frac{T_{H} }{T_{L} }$

$Q_{L,rev} = \frac{T_{L} }{T_{H} } Q_{H,rev}$

= $\frac{(30+273)K}{(652+273)K} (500KJ)$

= 164KJ

Carnot heat engine converts 67.2% of the heat it receives to work.

The amount of heat rejected to the sink per cycle = 164 kJ

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