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Thermodynamics

Question
CBSEENPH11020391

A Carnot engine, having an efficiency of η = 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

  • 99 J

  • 90 J

  • 1 J

  • 100 J

Solution

B.

90 J

straight W space equals space straight Q subscript 1 space open parentheses straight T subscript 1 over straight T subscript 2 minus 1 close parentheses space space space space straight eta space equals space 1 minus straight T subscript 2 over straight T subscript 1
10 space equals space straight Q subscript 2 space open parentheses 10 over 9 minus 1 close parentheses space space space space 1 over 10 space equals space 1 minus straight T subscript 2 over straight T subscript 1
rightwards double arrow space space straight T subscript 2 over straight T subscript 1 space equals 1 space minus 1 over 10 space equals space 9 over 10
10 space equals space straight Q subscript 2 space open parentheses 1 over 9 close parentheses
rightwards double arrow space straight T subscript 1 over straight T subscript 2 space equals space 10 over 9
straight Q subscript 2 space equals space 90 space straight J