Question

One reversible engine operates between 1600 k and t2 k and another reversible engine operates between t2 k and 400 k. if both engines have same heat input and output, then the temperature t2 must be equal to

Answer 1

According to question ,
It is mentioned that both engines have same heat input and output.
Means efficiency of both engines have same.
we know, efficiency of engine when temperature T₁ and T₂,
β = 1 - T₂/T₁
similarly efficiency of engine when temperature T₂ and T₃,
β = 1 - T₃/T₂

Now, 1 - T₂/T₁ = 1 - T₃/T₂
⇒ T₂/T₁ = T₃/T₂

Here, T₁ = 1600K , T₂ = t₂ K and T₃ = 400 K

Now, t₂/1600 = 400/t₂
⇒ t₂² = 640000K
taking square both sides,
t₂ = 800K
Hence, andwer is 800K