Two heat engines (X ) and (Y ) of same efficiency are connected in series in such a way that the sink of (X ) works as source of (Y . X ) receives heat at (900 ~K ) and rejects some heat to its sink at (T ~K ) and in turn (Y ) rejects heat

Question

Two heat engines (X ) and (Y ) of same efficiency are connected in series in such a way that the sink of (X ) works as source of (Y . X ) receives heat at (900 ~K ) and rejects some heat to its sink at (T ~K ) and in turn (Y ) rejects heat to its sink at (400 ~K ), then the temperature (T ) is

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Correct answer: B. (600 ~K )

According to the question, a series combination of two heat engines are shown in the figure below, Given, temperature of (X ) heat engine, (T₁=900 ~K ) and temperature of (Y ) heat engine, (T₂=400 ~K ) So, efficiency of (x ) heat engine, ( _x=1- T T₁ =1- T 900 ) Similarly, ( _y=1- T₂ T =1- 400 T ) ( ) Given, ( _x= _y ) ( aligned 1- T 900 & =1- 400 T T^2 & =900 400 T & =600 ~K aligned ) Hence, the correct option is (b).

Two heat engines (X ) and (Y ) of same efficiency are connected in series in such a way that the sink of (X ) works as source of (Y . X ) receives heat at (900 ~K ) and rejects some heat to its sink at (T ~K ) and in turn (Y ) rejects heat to its sink at (400 ~K ), then the temperature (T ) is

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