# How much does air volume change with temperature?

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If I have a closed cylinder with a fixed air volume inside and a piston on the open end I need to calculate how much the piston will move as the temperature changes through a range of 100 degrees F?

Air volume vs temperature?

olivermsun
Is there some kind of resistance to the piston moving out from the outset? Outside air pressure at the same temperature?

Presumably you're saying the piston is free to move but presently is not moving, implying that the pressure on either side of the piston is the same. When you raise the temperature inside the cylinder the pressure will increase which will move the cylinder until the pressure inside is once again equal to the outside.

You need to use the ideal gas law: PV = nRT. This should give you a good approximation of how much the volume will expand, since you can assume the pressure before and after the temperature change are both going to be equal to the ambient (atmospheric?) pressure. Remember to use the correct value of R depending on the units you use; 0.08206 if you're using liters and amtomspheres; 8.314 if you're using pascals and cubic meters.

You will need to solve for n (moles of 'air molecules') using the initial state of your system before solving for the final volume.

Oh and don't forget that the temperature must be converted to absolute temperature in Kelvins.

Let us assume that air is an ideal gas.
We can use $V1/T1=V2/T2$ we have $deltaT=T2-T1$

I build 3 hot air engines by copying an existing 2" bore engine. Engine is very low power there can be no piston friction or it will not run. Piston diameter is 1.9985" and bore diameter is 2.0000". The piston has .020" grooves around the diameter 1/8" apart. I can not remember the scientific name for the grooves but they act like zero fiction piston rings. Piston is light weight aluminum and cylinder is cast iron. Start the engine at room temperature the 2 metals have a different expansion rate clearance is .0015" at room temperature and .0005" when the engine is hot about 500 degrees F. The engine runs 500 RPMs with the blade and 900 to 1200 RPMs with no blade. See attached youtube videos

This is the original 1917 Al-Cool Fan.

This is a copy of the original FAN it runs 450 RPMS. The base is a zinc sand casting of a salad bowl.

This is a Gear Drive engine it runs 450 RPMs with the fan blade.

This is a factory engine it runs 900 to 1200 RPMs real easy with no fan blade.

Let us assume that air is an ideal gas.
We can use $V1/T1=V2/T2$ we have $deltaT=T2-T1$
Actually yeah, that's a lot more straightforward than what I said.

Micromike
I took engineering in college 50 years ago I have forgotten more than I every knew. I remember learning about Ideal gas Law but I don't remember PV=nRT? What is P, What is V, what is n, what is R, what is T. You know the saying, if you don't use it you loose it. A lot of what I learned in college I never used at work. I took math every semester in college only math class I did not take was, imaginary numbers. I have forgotten so much math its not funny.

P is pressure, V is volume, n is number of moles of molecules, R is the universal gas constant, T is temperature. That said, easier way to solve the problem you proposed would actually be Charles' law like Micromike said; V1/T1 = V2/T2.

So the ratio of initial and final temperature would give you the ratio of initial and final volumes; T2/T1 = V2/V1 or V2 = (V1T2)/T1

Since you're using a ratio you shouldn't need to convert temperature to Kelvins... I think. I would just to be safe though

Micromike
I don't know pressure and no way to measure it?

I can calculate volume.

Don't now n?

Don't know R?

I can measure temperature to a point plus or minus maybe 100 degrees.

This 1 cylinder has 2 pistons. The piston in the center of the cylinder does not tough the sides or top of bottom. There is a space of about 1/16" all the way round the displacer piston. When the displacer piston is up all the air is at the hot end of the cylinder about 600 degrees. Hot air expands pushing the power piston up. When displacer piston is at the bottom of the cylinder all the air is at the top COLD end of the cylinder where it cools contracts and sucks the power piston down. This is a 1 cycle beta stirling engine. After the engine runs for several minutes the top of the cylinder gets hot too I am guessing maybe 300 or 400 degrees. Once the engine is warmed up there is a temperature difference from bottom to top of maybe 200 or 300 degrees. Maybe I need to buy a laser thermometer to check both ends for exact temperature while the engine runs. Next engine I want a larger diameter piston and air or water cooling for the top. I put air cooling on 1 engine already it runs better. I did a few manual test pushing the displacer piston up/down by hand and measuring how much the power piston moves I am not getting accurate measurements.

Without knowing the temperature involved with more accurate increments than 100 degrees you can't really say how much the air will expand. If the outside of the piston is exposed to the open air, then the pressure is atmospheric pressure, about 100,000 Pa or 1 atm, give or take a little. Increasing the temperature of the air inside would increase the volume according to either of the two equations posted above.

If I understand you correctly, you have a temperature gradient from one end of the cylinder to the other. In a relatively small (i.e. not huge) cylinder it's hard to imagine why air at one end would be drastically different from air at the other end. Perhaps the metal at each end has different temperature, but the gas inside the cylinder would move around very quickly to equalize any considerable temperature or pressure difference.

Sorry if I'm misunderstanding something, perhaps a diagram of the inside of the cylinder would help? I'm not terribly familiar with stirling engines.

jbriggs444
Homework Helper
Since you're using a ratio you shouldn't need to convert temperature to Kelvins...
You need the temperature expressed on an absolute scale. e.g. Kelvin or Rankine. Not Celsius or Fahrenheit.

Nidum
Gold Member
The air in the engine is going through a cycle controlled by the motions of two pistons with a roughly 90 phase angle between them and by the effects of heat addition and extraction .

The volume of the contained air at particular point in the cycle of an engine of known geometry only depends on the positions of the pistons .

To work out the details of pressure variations in the engine you need to analyse the complete engine .

Start by getting to understand the theoretical thermodynamic cycle for a Stirling engine .

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Nidum
Gold Member
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Kaminska Zakrzewska
i’m going on a gut feeling here, but i’m gonna say .87 cents, that’s with all previous assumptions but only getting it there and not sustaining it

Here is a video that shows how a stirling hot air engine works. I am pretty sure air expands at a stead rate like other things. A 12" long steel rod will expand about .001" of an inch it temperature changes about 10 degrees F. Brass and aluminum expand at a different rate. Since air is a gas the volume changes, volume of a steel rods changes too but it is solid material. If air temperature increases 10 degrees volume should increase at a certain amount lets assume it increases 1%, then a heat increase of 100 degrees will make air volume increase 10%, and a heat increase of 200 degrees will make volume increase 20%.

See the video.

What percentage does air volume change with a temperature change of 100 degrees F.

olivermsun
Depends what percentage 100°F is of the original temperature.

70 degrees to 170 degrees

olivermsun