A Carnot heat engine has an efficiency of 10 %. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

Question

A Carnot heat engine has an efficiency of 10 %. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance. (A) 8 (B) 9 (C) 6 (D) 5

Tardigrade Admin · Accepted Answer

η=1-(T2/T1), (T1/T2)=(1/1-η) ω =(T2/T1-T2)=(1/(T1 / T2)-1) =(1/[1 /(1-η)]-1)=(1-η/η) As η =10 %=0.1, ω=(1-0.1/0.1)=9

Q. A Carnot heat engine has an efficiency of $10%$ . If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

8

9

6

5

$η = 1 - \frac{T _{2}}{T _{1}}, \frac{T _{1}}{T _{2}} = \frac{1}{1 - η}$
$ω = \frac{T _{2}}{T _{1} - T _{2}} = \frac{1}{( T _{1} / T _{2} ) - 1}$
$= \frac{1}{[ 1/ ( 1 - η )] - 1} = \frac{1 - η}{η}$
As $η = 10% = 0.1,$
$ω = \frac{1 - 0.1}{0.1} = 9$

Q. A Carnot heat engine has an efficiency of 10%. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

8

9

6

5

η=1−T1​T2​​,T2​T1​​=1−η1​ ω=T1​−T2​T2​​=(T1​/T2​)−11​ =[1/(1−η)]−11​=η1−η​ As η=10%=0.1, ω=0.11−0.1​=9

Q. A Carnot heat engine has an efficiency of $10%$ . If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

$η = 1 - \frac{T _{2}}{T _{1}}, \frac{T _{1}}{T _{2}} = \frac{1}{1 - η}$
$ω = \frac{T _{2}}{T _{1} - T _{2}} = \frac{1}{( T _{1} / T _{2} ) - 1}$
$= \frac{1}{[ 1/ ( 1 - η )] - 1} = \frac{1 - η}{η}$
As $η = 10% = 0.1,$
$ω = \frac{1 - 0.1}{0.1} = 9$