Question 417: Thermodynamics & KTG

Question

Three Carnot engines operate in series between a heat source at a temperature T
1
and a heat sink at temperature T
4
(see figure). There are two other reservoirs at temperature T
2
and T
3
, as shown, with T
1
> T
2
> T
3
> T
4
. The three engines are equally efficient if -

Accepted Answer

$${t_1} = 1 - {{{T_2}} \over {{T_1}}} = 1 - {{{T_2}} \over {{T_2}}} = 1 - {{{T_4}} \over {{T_3}}}$$
$$ \Rightarrow \,\,\,{{{T_2}} \over {{T_1}}} = {{{T_3}} \over {{T_4}}} = {{{T_4}} \over {{T_3}}}$$
$$ \Rightarrow \,\,\,{T_2} = \sqrt {{T_1}{T_3}}  = \sqrt {{T_1}\sqrt {{T_2}{T_4}} } $$
$${T_3} = \sqrt {{T_2}{T_4}} $$
$$T_2^{3/4} = \sqrt {T_1^{1/2}} T_4^{1/4}$$
$${T_2} = T_1^{2/3}T_4^{1/3}$$

Answer

T
2
= (T
1
3
T
4
)
1/4
;  T
3
= (T
1
T
4
3
)
1/4

Answer

T
2
= (T
1
T
4
)
1/2
;  T
3
= (T
1
2
T
4
)
1/3

Answer

T
2
= (T
1
T
4
2
)
1/3
;  T
3
= (T
1
2
T
4
)
1/3

Answer

T
2
= (T
1
2
T
4
)
1/3
;  T
3
= (T
1
T
4
2
)
1/3

Thermodynamics & KTG

Three Carnot engines operate in series between a heat source at a temperature T 1 and a heat sink at temperature T 4 (see figure). There are two other reservoirs at temperature T 2 and T 3 , as shown, with T 1 > T 2 > T 3 > T 4 . The three engines are equally efficient if -

Choose the correct answer: