Question 418: Thermodynamics & KTG

Question

Two Carnot 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 tum, 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 :

Accepted Answer

Here, Q
1
= W
1
+ Q
2
and  Q
2
= W
2
+ Q
3
Given that,
W
1
= W
2
$$ 	herefore $$  Q
1
$$-$$ Q
2
= Q
2
$$-$$ Q
3
$$ \Rightarrow $$  nC
v
(T
1
$$-$$ T
2
) = nC
v
(T
2
$$-$$ T
3
)
$$ \Rightarrow $$  T
1
$$-$$ T
2
= T
2
$$-$$ T
3
$$ \Rightarrow $$   T
2
= $${{{T_1} + {T_3}} \over 2}$$
= $${{600 + 400} \over 2}$$
= 500 K

Answer

600 K

Answer

400 K

Answer

300 K

Answer

500 K

Thermodynamics & KTG

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