The efficiency of a carnot engine is 1 6

Asked by admin @ 13/08/2021 in Physics viewed by 270 People

the efficiency of carnot engine is 1/6 if on reducing the temperature the temperature of sink by 65k the efficnecy becomes 1/3 find the intial and final temperature btween wich the cycle is workng

Answered by admin @ 13/08/2021

The efficiency of Carnot engine if T₁ and T₂ temperature are initial and final temperature .
$\eta=1-\frac{T_2}{T_1}$

condition 1 :- when η ( efficiency of engine ) = 1/6
then, 1/6 = 1 - T₂/T₁ ---------(1)

condition 2 : when temperature of sink is reduced by 65K then, η(efficiency of engine ) = 1/3
e.g, 1/3 = 1 - (T₂ - 65)/T₁ -----------(2)

solve equations (1) and (2)
2(1 - T₂/T₁) = 1 - (T₂ - 65)/T₁
2 - 1 = 2T₂/T₁ - (T₂ - 65)/T₁ = (T₂ + 65)/T₁
T₁ = T₂ + 65
Put it in equation (1)
1/6 = 1 - T₂/(T₂ + 65)
1/6 = (65)/(T₂ + 65)
T₂ + 65 = 390 ⇒ T₂ = 325K or 52°C
now T₁ = 390K or 117°C

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