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Standard XII

Physics

Carnot Cycle

Two Carrnot e...

Question

Two Carrnot engines A and B are operated in series. The first one, A, receives heat at $T_{1} (= 600 K)$ and rejects to a reservoir at temperature $T_{2}$ . The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_{3} (= 400 K)$ . Calculate the temperature $T_{2}$ if the work outputs of the two engines are equal :

400 K

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600 K

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500 K

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300 K

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Solution

The correct option is B 500 K
According to above diagram,
$W_{1} = Q_{1} - Q_{2} W_{2} = Q_{2} - Q_{3} W_{1} = W_{2}$

So,
$Q_{1} - Q_{2} = Q_{2} - Q_{3} Q_{2} = \frac{Q_{1} + Q_{3}}{2}$

Or,
$T_{2} = \frac{T_{1} + T_{3}}{2}$

$T_{2} = \frac{600 + 400}{2} = 500 K$

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Similar questions

Q. Two carnot engines

A

and

B

are operated in series. The first one,

A

received heat at

T_{1} (= 600 K)

and rejects to a reservoir at temperature

T_{2}

. The second engine

B

receives heat rejected by the first engibe and in turn, rejects to a heat reservoir at

T_{3} = (400 K)

. Calculate the temperature

T_{2}

if the work outputs of the two engines are equal

Q. Two Carnot engines

A

and

B

are operated in series. The first engine,

A

, receives heat at

800 K

and rejects to a reservoir at temperature

T

. The second engine

B

receives the heat rejected by the first engine and in turn rejects to a heat reservoir at

300 K

. Find the value of

T

, when the work outputs of the engines are equal.

Q. Two Carnot engines

A

and

B

are operated in series. The first engine

A

, receives heat at

800 K

and rejects to a reservoir at temperature

T

. The second engine

B

receives the heat rejected by the first engine and in turn rejects to a heat reservoir at

300 K

. Find the value of

T

, when the work outputs of the engines are equal.

Q. Two Carnot engines A and B are operated in series. The first one A receives heat at 800 K and rejects to a reservoir at temperature T. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 300 K. Calculate the temperature T for the following situations:
(a) The outputs of the two engines are equal and
(b) The efficiencies of two engines are equal

Q. Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at

T_{1}

=800 K and rejects to sink at

T_{2}

K. The second engine B receives heat rejected by the first engine and rejects to another sink at

T_{3}

=300 K If the work outputs of two engines are equal, then the value of

T_{2}

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The correct option is B 500 KAccording to above diagram,W1=Q1−Q2W2=Q2−Q3W1=W2So,Q1−Q2=Q2−Q3Q2=Q1+Q32Or,T2=T1+T32T2=600+4002=500 K

The correct option is B 500 K
According to above diagram,
$W_{1} = Q_{1} - Q_{2} W_{2} = Q_{2} - Q_{3} W_{1} = W_{2}$

So,
$Q_{1} - Q_{2} = Q_{2} - Q_{3} Q_{2} = \frac{Q_{1} + Q_{3}}{2}$

Or,
$T_{2} = \frac{T_{1} + T_{3}}{2}$

$T_{2} = \frac{600 + 400}{2} = 500 K$