How to calculate the efficiency of anything

  • Thread starter daisyi
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Since the steam is at 500C or 773K and the exhaust is at 20C or 293K, the efficiency of this engine would be:\eta = \frac{773K-293K}{773K} = 0.62 or 62%In summary, the boiler of a steam engine produces steam at a temperature of 500C, while the engine exhausts its waste heat into the atmosphere at a temperature of 20C. Assuming the efficiency of an engine can never be greater than that of a Carnot engine, the limiting efficiency of this engine is 62%. This is calculated by using the Carnot cycle efficiency formula, which takes into account the hot and cold temperatures of the engine.
  • #1
daisyi
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The boiler of a steam engine produces steam at a temperature of 500C. The engine exhausts its waste heat into the atmosphere where the temperature is 20C. Assuming that the efficiency of an engine can never be greater than that of a Carnot engine, what is the limiting efficiency of this engine?

I don't even know where to start with this one, I'm not sure that I understand how to calculate the efficiency of anything unless I know that it is a Carnot cycle or an Otto cycle.
 
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  • #2
Carnot cycle efficiency

daisyi said:
I don't even know where to start with this one, I'm not sure that I understand how to calculate the efficiency of anything unless I know that it is a Carnot cycle or an Otto cycle.
Since you are trying to find the limiting efficiency, treat it as a Carnot cycle. The efficiency of a Carnot cycle (which assumes an ideal reversible process) is:
[tex]\eta = \frac{T_{hot}-T_{cold}}{T_{hot}}[/tex]

where the temperatures are in degrees K.
 
  • #3
If this is referring to the efficiency of a steam engine, then the efficiency would be calculated by taking the work output of the engine divided by the heat input. In this case, the work output would be the mechanical work of the engine and the heat input would be the energy produced by the boiler. However, the efficiency of an engine can never be greater than that of a Carnot engine, which is the most efficient heat engine possible. The efficiency of a Carnot engine is calculated by taking the difference in temperature between the hot and cold reservoirs (in this case, 500C and 20C) and dividing it by the temperature of the hot reservoir (500C). So, the limiting efficiency of this engine would be (500C-20C)/500C, which equals 0.96 or 96%. This means that the efficiency of this engine cannot be greater than 96%.
 

1. What is efficiency and why is it important?

Efficiency is a measure of how well a system or process is performing in relation to its intended purpose. It is important because it helps us understand how effectively resources are being used and where improvements can be made.

2. How do you calculate efficiency?

Efficiency is calculated by dividing the output of a system or process by the input and multiplying by 100 to get a percentage. The formula is: Efficiency = (Output/Input) * 100%.

3. What factors can affect efficiency?

There are many factors that can affect efficiency, including human error, equipment malfunctions, and environmental conditions. Other factors such as design flaws, lack of training, and inefficient processes can also impact efficiency.

4. How can efficiency be improved?

Efficiency can be improved by identifying and addressing the factors that are negatively impacting it. This can involve implementing new technologies, improving processes, providing training, and regularly monitoring and evaluating performance.

5. Can efficiency be 100%?

In theory, efficiency can be 100%, meaning that all of the input is converted to output without any waste. However, in reality, it is nearly impossible to achieve 100% efficiency due to various factors such as friction, energy loss, and human error.

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