# Calculating Work Out for a Sterling Engine

• ofathens
In summary, the conversation discusses different methods for calculating the efficiency of a sterling engine. The formula for efficiency is given as n_th = W_out / Q_in, where Q_in is the heat input and W_out is the work output. One method proposed involves calculating the work output as a rotational analog of the definition of work. However, it is suggested that this may not be the most accurate method due to factors such as friction and air resistance. Another method involves using a wheel with low friction and a weight attached to it, and measuring the power output based on the weight's force and the wheel's rotation frequency. This method may provide more accurate results.
ofathens
I was reading a list of science experiment ideas, and came across one that intrigued me: calculating the efficiency of a sterling engine.

We can say that the efficiency n_th is:

n_th = W_out / Q_in

Assuming we are heating the engine with a beaker of hot water,

Q_in = m * c * $$\Delta$$T

But how would we calculate work out? If the engine is making a wheel spin, as most sterling engines do, then we could calculate the work out as a rotational analog of the definition of work:

W_out = $$\tau$$$$\Delta\theta$$

Where $$\tau$$ is the torque on the wheel, which we could substitute with

$$\tau$$ = $$\alpha$$I

Where $$\alpha$$ is the angular acceleration, and I is the moment of inertia of the wheel.

Thus, we must be able to calculate the angular acceleration of the wheel, as well as its moment of inertia. Is this the easiest way to do this? How else could we measure the effieciency of a sterling engine?

Calculating work put into kinetic energy of a wheel would almost certainly give very poor results, because:

1. You need a long time to measure input heat accurately (you need to asume that input heat is much larger than the change of internal energy of the engine). However you can't accelerate a wheel with the full engine's power for a long time, because of the friction and air resistance.

2. Moving parts inside the engine are also accelerating, so wheel does not get the full power.

I would rather chose this method:

Let the engine propel the wheel that has very little friction, but a rope carriing a weight with mass m is wrapped several times around the wheel. On one side rope should be hanging free (but strained with weigth force), on the other side it should be fixed. If the rope is wrapped so many times, that the force on the fixed point is negligible, then the force sloving down the wheel is:

F=m*g

And power is: P=m*g*v=m*g*2*Pi*r*rotation frequency

You would probably want to maximize power by selecting a proper weight mass (since the rotation frequency will be dependent of the brake force)

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Calculating work out for a sterling engine involves measuring the amount of energy output by the engine, which can be done by measuring the torque and angular acceleration of the wheel. This can then be used to calculate the work output using the rotational analog of the definition of work. However, there are other ways to measure the efficiency of a sterling engine.

One alternative method is to measure the temperature difference between the hot and cold sides of the engine, as well as the rate of heat transfer. This would allow us to calculate the thermal efficiency of the engine, which is the ratio of the work output to the heat input. This method may be easier and more accurate than measuring torque and angular acceleration.

Another approach is to measure the pressure and volume changes in the engine using pressure sensors and displacement sensors. This would allow us to calculate the work output based on the changes in pressure and volume, and compare it to the heat input to determine the efficiency.

In addition, we could also consider the overall performance of the engine, such as its power output and mechanical efficiency, which takes into account factors like friction and losses in the engine.

Overall, there are multiple ways to measure the efficiency of a sterling engine, and it may be beneficial to use a combination of methods to get a more comprehensive understanding of its performance.

## 1. What is the Sterling Engine and how does it work?

The Sterling Engine is a type of heat engine that operates by cyclic compression and expansion of air or other gas at different temperatures. It works by using the temperature difference between a hot and cold source to drive the movement of a piston, which in turn powers the engine.

## 2. How do you calculate the work output of a Sterling Engine?

The work output of a Sterling Engine can be calculated by multiplying the change in volume of the gas by the pressure exerted on the piston. This can be represented by the equation W = PΔV, where W is the work output, P is the pressure, and ΔV is the change in volume.

## 3. What factors affect the work output of a Sterling Engine?

The work output of a Sterling Engine is affected by several factors such as the temperature difference between the hot and cold source, the type of gas used in the engine, the size and design of the engine, and the efficiency of the heat transfer process.

## 4. How can the efficiency of a Sterling Engine be improved?

The efficiency of a Sterling Engine can be improved by using a higher temperature difference between the hot and cold source, using a more efficient gas such as helium or hydrogen, and optimizing the design of the engine for better heat transfer.

## 5. Are there any limitations to the work output of a Sterling Engine?

Yes, there are limitations to the work output of a Sterling Engine. The maximum work output is limited by the maximum temperature difference that can be achieved between the hot and cold source, the type of gas used, and the efficiency of the engine. Additionally, the work output may decrease over time due to wear and tear or other factors affecting the engine's performance.

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