Question 990: Thermodynamics & KTG

Question

The (W/Q) of a Carnot engine is 1/6, now the temperature of sink is reduced by 62
o
C, then this ratio becomes twice, therefore the initial temperature of the sink and source are respectively

Accepted Answer

Initially the efficiency of the engine was
$${1 \over 6}$$ which increases to $${1 \over 3}$$ when the sink temperature reduces by 62ÃÂº C.
$$\eta  = {1 \over 6} = 1 - {{{T_2}} \over {{T_1}}}$$ when T
2
= sink temperature
, T
1
= source temperature
$$ \Rightarrow {T_2} = {5 \over 6}{T_1}$$
Secondly,
$${1 \over 3} = 1 - {{{T_2} - 62} \over {{T_1}}} = 1 - {{{T_2}} \over {{T_1}}} + {{62} \over {{T_1}}}$$
$$ = 1 - {5 \over 6} + {{62} \over {{T_1}}}$$
$$ \Rightarrow {T_1} = 62 	imes 6 = 372K = 372 - 273 = {99^o}C$$
& $${T_2} = {5 \over 6} 	imes 372 = 310K = 310 - 273 = {37^o}C$$

Answer

33
o
C, 67
o
C

Answer

37
o
C, 99
o
C

Answer

67
o
C, 33
o
C

Answer

97 K, 37 K

Thermodynamics & KTG

The (W/Q) of a Carnot engine is 1/6, now the temperature of sink is reduced by 62 o C, then this ratio becomes twice, therefore the initial temperature of the sink and source are respectively

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