    Question

# Two reversible heat engines A and B are arranged in series. A rejecting heat directly to B. Engine A receives 200 kJ at a temperature of 421 oC from a hot source, while B is in communication with a cold sink at temperature 4.4oC. If the work output of A is twice that of B. The intermediate temperature between A and B is

A
143.3oC
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B
212.7oC
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C
108.5oC
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D
170.5oC
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Solution

## The correct option is A 143.3oC WA=2WB Now, WAQ1=T1−T2T1......(i) ⇒WA=[T1−T2T1]×Q1.....(ii) WBQ2=T2−T3T2 Now, WB=T2−T3T2[Q1−WA][∵Q2=Q1−WA].....(iii) Putting value of equation (iii) in equation (i) ⇒WA=2[T2−T3]T2[Q1−WA] ⇒[T22(T2−T3)+1]WA=Q1 Putting value of equation (ii) in above equation ⇒[T2(T2−T3)2+1][T1−T2T1]Q1=Q1 ⇒T22T2−2T3=T1T1−T2−1=T2T1−T2 ⇒T1−T2=2T2−2T3 ⇒T2=T1+2T33=694+2×277.43=416.267K ⇒T2=143.3oC  Suggest Corrections  20    Join BYJU'S Learning Program
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