Question 380: Thermodynamics & KTG

Question

A Carnot engine has an efficiency of $${1 \over 6}$$. When the temperature of the sink is reduced by 62ºC, its efficiency
is doubled. The temperatures of the source and the sink are, respectively

Accepted Answer

$$\eta  = 1 - {{{T_2}} \over {{T_1}}}$$
$$ \Rightarrow $$ $${1 \over 6} = 1 - {{{T_2}} \over {{T_1}}}$$
$$ \Rightarrow $$ $${{{T_2}} \over {{T_1}}} = {5 \over 6}$$
When the temperature of the sink is reduced by 62ÃÂºC, then
$$\eta ' = 1 - {{{T_2} - 62} \over {{T_1}}}$$
$$ \Rightarrow $$ $$2 	imes {1 \over 6} = 1 - {{{T_2}} \over {{T_1}}} + {{62} \over {{T_1}}}$$
$$ \Rightarrow $$ $${1 \over 3} = {1 \over 6} + {{62} \over {{T_1}}}$$
$$ \Rightarrow $$ T
1
= 372 K = 99
o
C
T
2
= $${5 \over 3} 	imes 372$$ = 310 K = 37
o
C

Answer

99
o
C, 37
o
C

Answer

124
o
C, 62
o
C

Answer

37
o
C, 99
o
C

Answer

62
o
C, 124
o
C

Thermodynamics & KTG

A Carnot engine has an efficiency of ${1 \over 6}$. When the temperature of the sink is reduced by 62ºC, its efficiency is doubled. The temperatures of the source and the sink are, respectively

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