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 :
Solution
T<sub>2</sub> = sink temperature<br><br>$\eta = 1 - {{{T_2}} \over {{T_1}}}$<br><br>${1 \over 4} = 1 - {{{T_2}} \over {{T_1}}}$<br><br>${{{T_2}} \over {{T_1}}} = {3 \over 4}$ .... (i)<br><br>${1 \over 2} = 1 - {{{T_2} - 58} \over {{T_1}}}$<br><br>${{{T_2}} \over {{T_1}}} = {{58} \over {{T_1}}} = {1 \over 2}$<br><br>${3 \over 4} = {{58} \over {{T_1}}} + {1 \over 2}$<br><br>${1 \over 4} = {{58} \over {{T_1}}} \Rightarrow {T_1} = 232$<br><br>${T_2} = {3 \over 4} \times 232$<br><br>${T_2} = 174$ K
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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