How come heat engines are more efficient when run at high temperatures?
Carnot efficiency = 100 * (Th-Tc)/Th
the bigger Th, the closer your efficiency can be to 100%
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html
Heat engines are more efficient when run at high temperatures due to a fundamental concept known as the Carnot efficiency. The efficiency of a heat engine is defined as the ratio of the useful work output to the heat energy input.
To understand why high temperatures yield higher efficiency, we need to consider the Carnot cycle. The Carnot cycle is an idealized thermodynamic process that consists of four reversible steps: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
According to the Carnot efficiency formula, the efficiency of a heat engine is given by:
Efficiency = 1 - (Tc/Th)
Where Tc is the absolute temperature of the cold reservoir (sink) and Th is the absolute temperature of the hot reservoir (source).
As we can see from the formula, the efficiency is inversely related to the temperature ratio. This means that the higher the temperature of the hot reservoir, the lower the temperature ratio, resulting in a higher efficiency.
Now, how can we relate this idea to real-world heat engines? Real engines do not operate according to the ideal Carnot cycle, but the Carnot efficiency provides an upper limit to the efficiency that can be achieved. By operating at high temperatures, heat engines can approach the Carnot efficiency and thus maximize their efficiency.
There are practical limitations to consider, such as the material properties and the ability to handle high temperatures without excessive wear, degradation, or safety hazards. However, technological advancements are constantly being made to overcome these challenges and increase the efficiency of heat engines.