CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at T1=800 K and rejects to a sink at T2 K . The second engine B receives heat rejected by the first engine and rejects it to the another sink at T3=300 K. If the work outputs of the two engines are equal, then the value of T2 is
 
  1. 100 K
  2. 300 K
  3. 550 K
  4. 700 K


Solution

The correct option is C 550 K
If both carnot engines A & B are operated in succession, then sink of engine A will act as the source of engine B.
ηA=1T2T1=T1T2T1
Also for a carnot's engine,
TQ
T1T2Q1Q2
From energy conservation,
Q1=Q2+W
W=Q1Q2
ηA=T1T2T1=WAQ1 ....(1)
Similarly for engine B, the temperature of source is T2 and that of sink is T3.
ηB=T2T3T2=WBQ2 ....(2)
Also work output of both engine is same i.e WA=WB
Taking the equation (2) and (1),
Q1Q2=T1T2×T2T3T1T2
For a carnot's engine, Q1Q2=T1T2
Hence on equating above equations we get,
T1T2×T2T3T1T2=T1T2
2T2=T1+T3
T2=T1+T32=11002=550 K

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image