Heat and Thermodynamics 5 Question 1

1. A Carnot engine has an efficiency of 1/6. When the temperature of the sink is reduced by 62C, its efficiency is doubled. The temperatures of the source and the sink are respectively,

(2019 Main, 12 April II)

(a) 62C,124C

(b) 99C,37C

(c) 124C,62C

(d) 37C,99C

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Solution:

  1. Efficiency of a Carnot engine working between source of temperature T1 and sink of temperature T2 is given by

η=1T2T1

Here, T2 and T1 are absolute temperatures.

Initially,

η=1616=1T2T1T2T1=56

Finally, efficiency is doubled on reducing sink temperature by 62C.

η=26,Tsink =T2=T262

So, η=1T2T1

26=1T262T1T262T1=46T2T162T1=465662T1=46T1=6×62=372K=372273=99CT2=56×T1310K=310273=37C[T2T1=56]



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