Question 355: Thermodynamics & KTG

Question

A reversible engine has an efficiency of $${1 \over 4}$$. If the temperature of the sink is reduced by 58$$^\circ$$C, its efficiency becomes double. Calculate the temperature of the sink :

Accepted Answer

T
2
= sink temperature
$$\eta  = 1 - {{{T_2}} \over {{T_1}}}$$
$${1 \over 4} = 1 - {{{T_2}} \over {{T_1}}}$$
$${{{T_2}} \over {{T_1}}} = {3 \over 4}$$ .... (i)
$${1 \over 2} = 1 - {{{T_2} - 58} \over {{T_1}}}$$
$${{{T_2}} \over {{T_1}}} = {{58} \over {{T_1}}} = {1 \over 2}$$
$${3 \over 4} = {{58} \over {{T_1}}} + {1 \over 2}$$
$${1 \over 4} = {{58} \over {{T_1}}} \Rightarrow {T_1} = 232$$
$${T_2} = {3 \over 4} 	imes 232$$
$${T_2} = 174$$ K

Answer

174$$^\circ$$C

Answer

280$$^\circ$$C

Answer

180.4$$^\circ$$C

Answer

382$$^\circ$$C

Thermodynamics & KTG

A reversible engine has an efficiency of ${1 \over 4}. If the temperature of the sink is reduced by 58^\circ$C, its efficiency becomes double. Calculate the temperature of the sink :

Choose the correct answer: