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Mechanical Properties Of Fluids

Question
CBSEENPH11019821

Carnot engine takes 90 cal of heat from the reservoir at temperature 540K. Engine performs 126J of work. To increase the engine performance to 150J, to what temperature the hot reservoir should be raised?

Solution

Given,
Heat space taken space from space the space reservoir comma space straight Q subscript 1 space equals space 90 space cal space equals space 378 straight J space

Work space done space by space the space engine comma space straight W space equals space 126 straight J
Heat released, straight Q subscript 2 space equals space 378 minus 126 space equals space 252 straight J         

                       straight T subscript 1 space equals space 840 space straight K
Since,
        straight Q subscript 1 over straight Q subscript 2 equals straight T subscript 1 over straight T subscript 2 
∴      space space straight T subscript 2 space equals space straight Q subscript 2 over straight Q subscript 1 straight T subscript 1 space equals space 252 over 378 cross times 540 space equals space 360 straight K 
Let at temperature space straight T subscript 1 apostrophe space comma  the engine's performance be 150J.
Thus, 
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and    space space straight Q subscript 2 apostrophe space equals space 378 minus 150 space equals space 238 straight J 
Now     straight T subscript 1 apostrophe space equals space fraction numerator straight Q subscript 1 apostrophe over denominator straight Q subscript 2 apostrophe end fraction straight T subscript 2 equals 378 over 228 cross times 360 space equals space 596.84 straight K
The hot reservoir should be raised to a temperature of 596.84 K.