Question 475: Thermodynamics & KTG

Question

Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4. 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

T2 = (T13T4)1/4;  T3 = (T1T43)1/4

Answer

T2 = (T1T4)1/2;  T3 = (T12T4)1/3

Answer

T2 = (T1T42)1/3;  T3 = (T12T4)1/3

Answer

T2 = (T12T4)1/3;  T3 = (T1T42)1/3

Thermodynamics & KTG

Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4. The three engines are equally efficient if -

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