One of the most efficient engines ever built is
a coal-fired steam turbine in the Ohio valley,
driving an electric generator as it operates
between 1870�C and 430�C.
What is itsmaximumtheoretical efficiency?
To calculate the maximum theoretical efficiency of a heat engine, we can use the Carnot efficiency formula.
The Carnot efficiency is given by:
Efficiency = 1 - (Tc / Th)
Where:
Efficiency is the maximum theoretical efficiency of the heat engine,
Tc is the temperature at the colder side, and
Th is the temperature at the hotter side.
In this case, the temperature range given is 1870°C (2143 Kelvin) to 430°C (703 Kelvin).
Using the formula, we can calculate the maximum theoretical efficiency as follows:
Efficiency = 1 - (Tc / Th)
Efficiency = 1 - (703 / 2143)
Efficiency ≈ 1 - 0.3279
Efficiency ≈ 0.6721
Therefore, the maximum theoretical efficiency of the coal-fired steam turbine in the Ohio Valley is approximately 67.21%.
To determine the maximum theoretical efficiency of the coal-fired steam turbine, we need to use the Carnot efficiency formula. The Carnot efficiency represents the maximum possible efficiency of any heat engine operating between two given temperatures.
The formula to calculate the Carnot efficiency is:
Efficiency = 1 - (Tc/Th)
Where:
- Efficiency represents the maximum theoretical efficiency, expressed as a decimal.
- Tc represents the absolute temperature of the cold reservoir (in Kelvin).
- Th represents the absolute temperature of the hot reservoir (in Kelvin).
In this case, we are given the operating temperature range of the steam turbine: between 1870�C and 430�C. To convert these temperatures to Kelvin, we add 273.15 to each value.
Tc = 430�C + 273.15 = 703.15 K
Th = 1870�C + 273.15 = 2143.15 K
Now, we can plug these values into the Carnot efficiency formula:
Efficiency = 1 - (703.15 K / 2143.15 K)
By performing the division and subtraction, we can calculate the maximum theoretical efficiency of the coal-fired steam turbine.