Question

The efficiency of carnots cycle is 1/6 .if one reducing the temp of the sink by 65°C the efficiency becomes 1/3 find the initial and final temp between which the cycles is working

Answer 1

The efficiency of Carnot engine if T¹ and T² temperature are initial and final temperature .

n=1-T²/T¹

condition 1 :- when n ( efficiency of engine ) = 1/6

then, 1/6 = 1 - T₂/T₁ ---------(1)

condition 2 : when temperature of sink is reduced by 65K then, n(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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