A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127°C and rejects 600J of heat energy during each cycle. The efficiency of engine and temperature of sink will be
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Given:
Heat absorbed, Q
1
=1000J
Heat rejected, Q
2
=600J
Temperature of reservoir, T
1
=127°C=127+273=400K
To find:
Efficiency of the engine, η=?
Temperature of sink, T
2
=?
Amount of useful work done per cycle, W=?
We know,
Efficiency of Carnot engine can be found be using the following formula,
η=
Q
1
Q
1
−Q
2
=
1000
1000−600
=0.4 or 40%
Hence, the efficiency of the engine is 40%
We know, Efficinecy of carnot engine is also equal to
η=
T
1
T
1
−T
2
∴0.4=
400
400−T
2
⟹400−T
2
=160
⟹T
2
=400−160=240K or 240−273=−33°C
Hence, the temperature of the sink is -33°C.
We know,
W=Q
1
−Q
2
=1000−600=400J
Hence the amount of useful work done during each cycle is 400J.
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