Question 558: Thermodynamics & KTG

Question

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 __________.

Accepted Answer

$$\because$$ $$n = {w \over {{Q_{in}}}} = {1 \over 4}$$
$${1 \over 4} = 1 - {{{T_1}} \over {{T_2}}}$$
$${{{T_1}} \over {{T_2}}} = {3 \over 4}$$
When the temperature of the sink is reduced by 52K then its efficiency is doubled.
$${1 \over 2} = 1 - {{\left( {{T_1} - 52} \right)} \over {{T_2}}}$$
$${{{T_1} - 52} \over {{T_2}}} = {1 \over 2}$$
$${{{T_1}} \over {{T_2}}}{{ - 52} \over {{T_2}}} = {1 \over 2}$$
$${3 \over 4} - {{52} \over {{T_2}}} = {1 \over 2}$$
$${{52} \over {{T_2}}} = {1 \over 4}$$
$${T_2} = 208$$ K

Thermodynamics & KTG

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 __________.

Integer / Numeric Answer Type