An ideal Carnot engine is working between 227°C and 77°C. This engine delivers power of lOkW. Find the rate at which engine rejects the heat to the sink.

Solution

Here,
Lower temperature, $straight T subscript 1 space equals space 227 degree straight C space equals space 500 straight K$
Temperature, $straight T subscript 2 space equals space 102 degree straight C space equals space 375 straight K$
The efficiency of engine is,
   $straight eta space equals space 1 minus straight T subscript 2 over straight T subscript 1 equals 1 minus 375 over 500 equals 0.25$
Since,    $straight eta equals straight W over straight Q subscript 1$
Therefore, the quantity of heat received by engine from source per second is,
$space space space space space space straight Q subscript 1 equals straight W over straight eta equals fraction numerator 10 comma 000 over denominator 0.25 end fraction equals 40 comma 000 space straight J divided by straight s$
Now the heat rejected to sink per second,
$straight Q subscript 2 space equals space straight Q subscript 1 minus straight W$
   $equals 40000 minus 10000 equals space 30000 straight J divided by straight s$