  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  100 K300 K550 K700 K

Solution

## The correct option is C 550 KIf both carnot engines A & B are operated in succession, then sink of engine A will act as the source of engine B. ηA=1−T2T1=T1−T2T1 Also for a carnot's engine, T∝Q ⇒T1−T2∝Q1−Q2 From energy conservation, Q1=Q2+W ⇒W=Q1−Q2 ∴ηA=T1−T2T1=WAQ1 ....(1) Similarly for engine B, the temperature of source is T2 and that of sink is T3. ηB=T2−T3T2=WBQ2 ....(2) Also work output of both engine is same i.e WA=WB Taking the equation (2) and (1), Q1Q2=T1T2×T2−T3T1−T2 For a carnot's engine, Q1Q2=T1T2 Hence on equating above equations we get, ⇒T1T2×T2−T3T1−T2=T1T2 ⇒2T2=T1+T3 ∴T2=T1+T32=11002=550 K  Suggest corrections   