Answer:
[tex]\frac{4}{3}[/tex]
Explanation:
Heat engine converts heat energy into work. Heat flows into the Carnot engine from the furnace and some of the heat is converted into work while the rest is expelled to the environment.
The efficiency of the Carnot engine = Work done by the engine ÷ Heat from the hot reservoir
η [tex]= \frac{W}{Q_{H}}[/tex]
Carnot engine is the most efficient heat engine because it consists of isothermal and adiabatic processes (reversible processes). However, it is not capable of converting all of the input heat into work. The leak decreases its efficiency.
Carnot Efficiency [tex]= \frac{T_{H} - T_{C}}{T_{H}}[/tex]
Carnot Efficiency [tex]= 1 -\frac{T_{C}}{T_{H}}[/tex]
Where;
[tex]T_{H}[/tex] = The temperature of the hot reservoir
[tex]T_{C}[/tex] = The temperature of the cold reservoir
0.25 [tex]= 1 -\frac{T_{C}}{T_{H}}[/tex]
[tex]\frac{T_{C}}{T_{H}}[/tex] = 1 - 0.25
[tex]\frac{T_{C}}{T_{H}}[/tex] = 0.75
[tex]\frac{T_{C}}{T_{H}}[/tex] = [tex]\frac{75}{100}[/tex]
[tex]\frac{T_{C}}{T_{H}}[/tex] = [tex]\frac{3}{4}[/tex]
[tex]\frac{T_{H}}{T_{C}}[/tex] = [tex]\frac{4}{3}[/tex]
Since a Carnot engine is a perfect heat engine,
The temperature of the hot reservoir, [tex]T_{H}[/tex] = The heat that flows into the Carnot engine [tex]Q_{H1}[/tex]
The temperature of the cold reservoir
, [tex]T_{C}[/tex] = The heat that flows directly to the environment [tex]Q_{H2}[/tex]
[tex]\frac{Q_{H1}}{Q_{H2}}=[/tex] [tex]\frac{4}{3}[/tex]
