# Expansion of air vs water

Xilus
Lets say you have a jar of water, and a jar of air.
You heat both of them 100C

will either of them explode?

ok just kidding.

which one exerts more pressure, and is hence more likely to explode?

did heating the substance turn heat into force? (force per unit area)

Staff Emeritus
2022 Award
Lets say you have a jar of water, and a jar of air.
You heat both of them 100C

will either of them explode?

100 C is the boiling point of water, so it's very likely to explode when the water boils into steam. As for the jar of air, it may or may not, depending on the strength of the jar. I wouldn't try it at home, that's for sure.

did heating the substance turn heat into force? (force per unit area)

No, but it does increase the force on the jar since the molecules are moving about faster.

Gold Member
Why not try to work out what the pressure rises would actually be for some sample problems ?

Chestermiller
Xilus
PV=nRT

Xilus
the constant R doesn't work with a liquid like water.
we could calculate the pressure for the air though! that's awesome.

Mentor
Is the jar initially full of water, or is the headspace. If the latter, is there air in the head space, or just water vapor?

Xilus
Xilus

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Gold Member
The effect with a totally full bottle would depend both on the expansion coefficient of the water and the glass of the bottle.

JRMichler and Xilus
Xilus
The apples were cooked in boiling water. so they probably absorbed a lot of water. that's why i chose water. of course there is lots of other biomass in the applesauce.

Mentor
The apples were cooked in boiling water. so they probably absorbed a lot of water. that's why i chose water. of course there is lots of other biomass in the applesauce.
How did you determine that there is absolutely no heat space and that you got all the air out when you put the lid on?

Mentor
There was a little air at the top. not much.
How much? The volume of liquid water only increases by about 4% when heated from 20 C to 100 C.

Xilus
Mentor
I'm guessing that, in this typical canning operation, there actually is a small amount of head space to begin with, and that the liquid in the jar is fairly hot when the lid goes on, rather than being cold. What is the temperature at filling? I would like to estimate the pressure of the jar contents when the temperature is at 100 C? I have done this kind of calculation before when the company I was at was working on the development of plastic soup cans for use by a food manufacturer.

I have seen canning done by boiling the apples in an open kettle, separately boiling (to sterilize) the jars and lids, then filling the jars hot and immediately putting on the lids. The resulting vacuum sucks down the lids. The sucked down lid shows that everything was done hot, and that you have a vacuum seal.

Xilus
Homework Helper
In a home canning operation, one is not supposed to tighten the rings until the jars are removed from the hot water bath. The operating principle is (I assume) based on water evaporating into the head space and displacing the air there. The excess gas should bubble out through the loose seal. As the jars are cooled, the water vapor condenses and the lids are pulled down tightly -- a "vacuum seal".

The head space gives you a nice pressure reduction without a great deal of cooling and associated volume reduction in the liquid contents.

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JRMichler
It's easy to calculate the pressure with some simplifying assumptions:

Start at 20 deg C, heat to 100 deg C.
Jar and lid are infinitely stiff, and have zero coefficient of thermal expansion.
Zero air in the water, zero air in headspace.

Density of water at 20 deg C and 1 bar is 998.23 kg/m^3.
Density of water at 100 deg C and 950 bar is 997.85.
Density of water at 100 deg C and 1000 bar is 999.70.
Interpolate to 998.23, pressure is 960 bar.
960 bar X 14.5 = 13,900 PSI. This is an upper limit because it does not include thermal expansion of the glass jar, and elastic deformation of the jar and lid, or the effect of air in the head space.

Adding in the effect of thermal expansion of the glass, and the elastic modulus of the glass and lid, will reduce the pressure. But the pressure will still be high enough to break any normal glass jar. Air in a head space is needed to save the jar.

Xilus
Xilus
i computed 18.71 PSI for the jar of air at 100C
its lower than i expected.