Question 960: Thermodynamics & KTG

Question

Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T
1
and rejects the heat to the sink at temperature T.  The second engine B receives the heat at temperature T and rejects to its sink at temperature T
2
. For what values of T the efficiencies of the two engines are equal

Accepted Answer

Efficiency of engine A,  $${\eta _1} = 1 - {T \over {{T_1}}}$$
Efficiency of engine B,  $${\eta _2} = 1 - {{{T_2}} \over T}$$
Here, $${\eta _1} = {\eta _2}$$
$$ 	herefore {T \over {{T_1}}} = {{{T_2}} \over T} \Rightarrow T = \sqrt {{T_1}{T_2}} $$

Answer

$${{{T_1} - {T_2}} \over 2}$$

Answer

$${T_1}{T_2}$$

Answer

$$\sqrt {{T_1}{T_2}} $$

Answer

$${{{T_1} + {T_2}} \over 2}$$

Thermodynamics & KTG

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