# Pls answer this Carnot engine mains question Q 5. Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two engines A and B are represent ed by $\eta$ A and  $\eta$ B , respectively, then what is the value of $\frac{{\eta }_{B}}{{\eta }_{A}}?$ Option :

Dear Student,

Let the output of both engines be W

Let the 1st engine take Q1 heat as input at temperature T1 = 600K and gives out heat Q2 at temperature T the second engine receive Q2 as input and give out Q3 at temperature T3 = 100k to the sink.

Work done by first engine W =  Q1 – Q2

Work done by 2nd engine W = Q2 – Q3

Thus,

Q1 – Q2 = Q2 – Q3

Dividing both sides by Q1

1 – Q2/Q1  = Q2/Q1 – Q3/Q1

=> 1-T/T1 = Q2/ Q1(1- Q3/ Q2)

=> 1-T/T1 = Q2/ Q1(1- T3/ T)

=>  1-T/T1 = T/T1 (1- T3/ T)

=> T1/T – 1 = 1 - T3/ T

=> T1/T + T3/ T = 2

=> 1/T (T1 + T3) = 2

=>T = (T1 + T3)/2

=> T = (600+100)/2 =350 K

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