An electrical generating plant operates at a boiler temperature of 220 deg C and exhausts the unused heat into a nearby river at 18 deg C. what is the maximum theoretical efficiency of the plant?
Well, to calculate the maximum theoretical efficiency of the plant, we need to channel our inner Einstein! So, grab your thinking cap and let's dive in!
The maximum theoretical efficiency of any heat engine can be determined by the Carnot Efficiency Formula:
Efficiency = 1 - (Tc/Th)
Here, Tc represents the temperature of the cold reservoir (in this case, the river) and Th represents the temperature of the hot reservoir (the boiler temperature).
So, let's plug in the numbers: Tc = 18°C and Th = 220°C
Efficiency = 1 - (18/220)
Calculating it gives us Efficiency = 0.9181 or approximately 91.81%
So, the maximum theoretical efficiency of the plant is 91.81%. Keep in mind that this is just the theoretical maximum, and in reality, there are various factors that can affect the actual efficiency of the plant. But hey, at least we got our math right!
To find the maximum theoretical efficiency of the plant, we can use the Carnot efficiency formula:
Carnot Efficiency = 1 - (Tc/Th)
Where:
Tc = temperature of the cold reservoir (in Kelvin)
Th = temperature of the hot reservoir (in Kelvin)
First, let's convert the given temperatures from degrees Celsius to Kelvin:
Tc = 18 + 273 = 291 K (temperature of the cold reservoir)
Th = 220 + 273 = 493 K (temperature of the hot reservoir)
Now, we can calculate the Carnot efficiency:
Carnot Efficiency = 1 - (Tc/Th)
= 1 - (291/493)
≈ 1 - 0.59
≈ 0.41 or 41%
Therefore, the maximum theoretical efficiency of the plant is approximately 41%.
To calculate the maximum theoretical efficiency of the plant, we can use the concept of Carnot efficiency. Carnot efficiency represents the maximum efficiency that can be achieved by any engine operating between two temperature extremes.
The formula for calculating Carnot efficiency is:
Efficiency = 1 - (Tc/Th)
Where:
- Efficiency is the maximum theoretical efficiency
- Tc is the temperature of the cold reservoir (18 °C converted to Kelvin, which is 18 + 273 = 291 K)
- Th is the temperature of the hot reservoir (220 °C converted to Kelvin, which is 220 + 273 = 493 K)
Substituting the values into the formula:
Efficiency = 1 - (291 / 493)
= 1 - 0.59
= 0.41, which is equivalent to 41%
Therefore, the maximum theoretical efficiency of the plant is 41%.
η =1 –T(cold)/T(hot) =
= 1- (273+18)/(273+22) =
=1-291/493 = 0.41