A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be __________.
Answer (integer)
208
Solution
$\because$ $n = {w \over {{Q_{in}}}} = {1 \over 4}$<br><br>${1 \over 4} = 1 - {{{T_1}} \over {{T_2}}}$<br><br>${{{T_1}} \over {{T_2}}} = {3 \over 4}$<br><br>When the temperature of the sink is reduced by 52K then its efficiency is doubled.<br><br>${1 \over 2} = 1 - {{\left( {{T_1} - 52} \right)} \over {{T_2}}}$<br><br>${{{T_1} - 52} \over {{T_2}}} = {1 \over 2}$<br><br>${{{T_1}} \over {{T_2}}}{{ - 52} \over {{T_2}}} = {1 \over 2}$<br><br>${3 \over 4} - {{52} \over {{T_2}}} = {1 \over 2}$<br><br>${{52} \over {{T_2}}} = {1 \over 4}$<br><br>${T_2} = 208$ K
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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