Question

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 a sink at T2K. The second engine B receives heat rejected by the first engine (A) and rejects to another sink at T3=200K. If the efficiencies of two engines are equal, then the value of T2 is​

Answer 1

11th/Physics

Thermodynamics

Answer :

Carnot engine A :

• Temp. of source (T₁) = 800K
• Temp. of sink (T₂) = T K

Carnot engine B :

• Temp. of source (T₁) = T K
• Temp. of sink (T₂) = 200K

Both engines have equal efficiency. We have to find the value of T₂$.$

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◈ Efficiency of carnot engine is given by

• η = 1 - T'/T

where,

T' denotes temperature of sink

T denotes temperature of source

✪ Efficiency of engine A :

➝ η₁ = 1 - T₂/T₁

➝ η₁ = 1 - T₂/800

✪ Efficiency of engine B :

➝ η₂ = 1 - T₃/T₂

➝ η₂ = 1 - 200/T₂

ATQ, η₁ = η₂

⇒ 1 - T₂/800 = 1 - 200/T₂

⇒ T₂/800 = 200/T₂

⇒ T₂² = 800 × 200

⇒ T₂² = 160000

⇒ T₂ = 400K

Cheers!