Efficiency of a heat engine is 1/6 on reducing the temperature of the sink by 65 degree Celsius the efficiency becomes 1/3. Find the initial temperature of the sink and the source.
Answers
Formula :
We know that :
Efficiency = 1 - T2 / T1
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Given information :
η = 1/6 initially
when T2 is reduced by 65°C then η becomes 1/3
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Solution
η = 1/6
==> 1 - T2 / T1 = 1/6 [ using the Formula ]........................(1)
When η = 1/3 :
η = 1 - ( T2 - 65 ) / T1
==> 1/3 = 1 - (T2 - 65)/T1.........................(2)
==> T2 - T1 = -65 [ because T2 is reduced by 65°C ]
==> T2 = T1 - 65...........................(3)
Put this in (2) :
==> 1/3 = 1 - ( T1 - 65 - 65 ) / T1
==> 1/3 = 1 - (T1 - 130 ) /T1
==> (T1 - 130) / T1 = 1 - 1/3
==> ( T1 -130 ) / T1 = 2/3
==> 3 ( T1 - 130 ) = 2 T1
==> 3 T1 - 390 = 2 T1
==> T1 = 390
The temperature initially was 390°C
Hope it helps you ^_^
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