[Supervolant (OP)]

Hello,

I would like to know how to calculate the thermal expansion / contraction of air by volume.

Please note that I am not a mathematician but more the kind of visual imaginative personality. Please try explaining it in pictures / words rather then just numbers. Do it Einstein style! ;-)

I want to calculate the followings two thermal expansions of air by volume.

One I call January is from -2,8 degree Celsius to +100 degree Celsius.

The other one Is Juli from +21,8 degree Celsius to +100 degree Celsius.

I have already researched a bit and tried my best to solve it myself but the Internet seems to be full of different formulas not really explaining it's single parts...

...Can someone help not only solving the challenges but also explaining the why?

https://en.wikipedia.org/wiki/Thermal_expansion

Even Wikipedia doesn't explain what it's single members of the formula mean.

Thanks already! :-)

[Supervolant (OP)]

I found this other Forum entry.

https://www.physicsforums.com/threads/how-much-does-air-expand-with-heat.267530/

I can't find validation on the formula one of their members suggested:
"So if you go from 20->40 C, the pressure * volume increases by (40+273)/(20+273) or about 6%"

Is this true? Then the thermal expansion in January would be 26% and 38% in Juli. Would be cool but seems to easy! :-D

[Supervolant (OP)]

I am a fan of actually giving out the solution.

http://www.peacesoftware.de/einigewerte/luft.html

This German calculator works wonders. Just type in the different parameters and it easily calculates everything and more within seconds. I am german so it comes in handy for me...

Thermal expansion in January is 22% and in Juli 28%. Pretty cool! :-)

One can close this thread now.

[chris]

Glad you got the answer you were looking for, even if not from us!

[alancalverd]

Cool, but WRONG!

The July temperature rise is less than January, so the expansion must be less, not more!

Dry air is pretty close to an ideal gas at normal ambient temperatures. Absolute temperature T is about 273 + Celsius temperature. The volume ratio between T₁ and T₂ is T₂/T₁.  T₂ = 373

January T₁ = 275.8 so the ratio is 373/275.8 = 1.35, or 35% expansion

July T₁ = 294.8 so the ratio is 373/294.8 = 1.27, or 27% expansion.

Which is why hot air balloons fly better in winter.

[evan_au]

As a resident of the Antipodes, the answers seem reversed.
Around here, it's much hotter in January (maximum temperature averages 27C) than in July (average high is 16C).

[alancalverd]

And the explanation...

An ideal gas is one that does not change state (i.e. remains a gas) at all temperatures and pressures, and whose pressure x volume varies linearly with temperature.

We know that gases contract with decreasing temperature, so we define "absolute zero" T = 0 K as the theoretical temperature at which an ideal gas would have zero volume. Obviously it is a model concept as everything actually liquefies or solidifies below 4K, but it's good enough for aeronautics.

The Kelvin temperature scale uses intervals of Celsius degrees, and it turns out that 0°C ≈ 273K, so absolute temperature T = Celsius temperature + 273

So we can state that PV = RT where P = pressure, V = volume, R is a universal constant, and T is the absolute (Kelvin) temperature. Thus if the pressure remains constant, V₁/V₂ = T₁/T₂.

[Supervolant (OP)]

I didn't recognize my calculation flaw and now I know better. Thank you!

You guessed right, it's about aeronautics.

[alancalverd]

Enjoy! I used to fly a 64000 cu ft (1800 cu m) hot air balloon. Madness, but huge fun. Max envelope temperature was limited to 100 C in my youth but I'm sure modern materials will tolerate a bit more.

[Petrochemicals]

Some thing i remember reading was pressue of the atmosphere is considered to be constant for calculation purposes,  even though it changes a little it is pretty much around 1 atm all the time, the exeptions being small pressure centres, but on average its between 980 to 1020, so negligable ammounts.