Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at T1 =800K and rejects to sink at T2K. The second engine B receives heat rejected by the first engine and rejects to another sink at T3 = 300K . If the work outputs of two engines are equal, then the value of T2 is

ηA=T1−T2T1=WAQ1⇒ηB=T2−T3T2=WBQ2∴Q1Q2=T1T2×T2−T3T1−T2=T1T2 ∴WA=WB∴T2=T1+T32=800+3002=550K

Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at T1 =800K and rejects to sink at T2K. The second engine B receives heat rejected by the first engine and rejects to another sink at T3 = 300K . If the work outputs of two engines are equal, then the value of T2 is

ηA=T1−T2T1=WAQ1⇒ηB=T2−T3T2=WBQ2∴Q1Q2=T1T2×T2−T3T1−T2=T1T2 ∴WA=WB∴T2=T1+T32=800+3002=550K

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Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at T₁=800K and rejects to sink at T₂K. The second engine B receives heat rejected by the first engine and rejects to another sink at T₃ = 300K . If the work outputs of two engines are equal, then the value of T₂ is

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100K

300K

550K

700K

answer is C.

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Detailed Solution

$\begin{array}{l} η_{A} = \frac{T_{1} - T_{2}}{T_{1}} = \frac{W_{A}}{Q_{1}} \Rightarrow η_{B} = \frac{T_{2} - T_{3}}{T_{2}} = \frac{W_{B}}{Q_{2}} \\ ∴ \frac{Q_{1}}{Q_{2}} = \frac{T_{1}}{T_{2}} \times \frac{T_{2} - T_{3}}{T_{1} - T_{2}} = \frac{T_{1}}{T_{2}} ∴ W_{A} = W_{B} \\ ∴ T_{2} = \frac{T_{1} + T_{3}}{2} = \frac{800 + 300}{2} = 550 K \end{array}$