A heat engine operates between two reservoirs at temperatures of 19.7oC and 294oC. What is the maximum efficiency possible for this engine?
To find the maximum efficiency of the heat engine, we can use the Carnot efficiency formula:
Efficiency = 1 - (T_cold / T_hot)
Where:
- Efficiency is the maximum efficiency of the engine,
- T_cold is the temperature of the colder reservoir in Kelvin,
- T_hot is the temperature of the hotter reservoir in Kelvin.
To convert the temperatures from Celsius to Kelvin, we use the formula:
T_Kelvin = T_Celsius + 273.15
Given:
T_cold = 19.7oC = 19.7 + 273.15 = 292.85 K
T_hot = 294oC = 294 + 273.15 = 567.15 K
Using the Carnot efficiency formula:
Efficiency = 1 - (292.85 K / 567.15 K)
Calculating:
Efficiency = 1 - 0.5161
Efficiency = 0.4839 or 48.39%
Therefore, the maximum efficiency possible for this heat engine is 48.39%.
To determine the maximum efficiency of a heat engine operating between two reservoirs at different temperatures, we can use the Carnot efficiency formula.
The Carnot efficiency (η) is given by the equation:
η = 1 - (Tc/Th)
Where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
In this case, the cold reservoir temperature is 19.7oC and the hot reservoir temperature is 294oC.
However, in order to use this formula, we need to convert the temperatures to the Kelvin scale, because the Carnot efficiency formula uses absolute temperature.
To convert Celsius to Kelvin, we add 273.15.
So, the cold reservoir temperature in Kelvin (Tc) is (19.7 + 273.15) = 292.85 K.
And the hot reservoir temperature in Kelvin (Th) is (294 + 273.15) = 567.15 K.
Now we can substitute these values into the Carnot efficiency formula:
η = 1 - (292.85/567.15)
η = 1 - 0.516 = 0.484
Therefore, the maximum efficiency possible for this heat engine is 48.4% (0.484 or 48.4/100).