Question 297: 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^\circC, its efficiency becomes double. Calculate the temperature of the sink :

Choose the correct answer: