B Extrapolation of relationship of temperature and volume for gas

[PainterGuy]

Hi,

Originally, the absolute temperature was thought to be around -273 Celsius around 1750 and it was the result extrapolation of of ideal gas law as shown below. I find it hard to phrase my question. But the question is how come they were so confident that the relationship between the volume or pressure for an ideal gas law is going be stay linear until the very limit of absolute zero? One example comes to my mind of Hooke's Law. It is linear only to a certain limit therefore you just can't extrapolate the data. Could you please help me with it?

Source: http://www.passmyexams.co.uk/GCSE/physics/volume-temperature-relationship-of-gas-Charles-law.htmlHelpful links:
1: https://en.wikipedia.org/wiki/Absolute_zero#History
2: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.html
3: https://en.wikipedia.org/wiki/Timeline_of_low-temperature_technology

 

[kuruman]

Nobody was confident that the relationship would stay linear until the limit of absolute zero is reached. It's just an extrapolation using the ideal gas model. People knew that real gases liquefy and solidify when their temperatures are lowered.

 

[Baluncore]

The linear proportional relationship only held near room temperatures if a constant of about -273 C was assumed in the calculations.
Later it was confirmed to hold at lower temperatures.

 

[PainterGuy]

Later it was confirmed to hold at lower temperatures.

Thank you!

So, it was more of a fluke?! They just came up with a value for absolute zero using extrapolation believing that the relationship is going to stay linear until the very limit of absolute zero is reached. Not only it stayed linear and even liquefaction of gases and solidification of liquids didn't affect their assumption of linear relationship.

 

[anorlunda]

Yes, but temperature and volumes aren't the only measures. Have a look at
https://en.wikipedia.org/wiki/Third_law_of_thermodynamics

Historically, that caused a lot of consternation about what happens near absolute zero because quantum mechanics began to enter into the explanation.

This entertaining video digs a bit into the history.

 

[Baluncore]

So, it was more of a fluke?! They just came up with a value for absolute zero using extrapolation believing that the relationship is going to stay linear until the very limit of absolute zero is reached.

Not exactly. There was no fluke about it. They needed a constant to make the math work for their experimental temperatures. That constant is now called absolute zero.

They did not have to assume anything. As they gradually lowered the experimental temperature, in the search for what happens closer to absolute zero, they found that proportionality held and absolute zero remained the same as the original empirical constant.

 

[PainterGuy]

As they gradually lowered the experimental temperature, in the search for what happens closer to absolute zero, they found that proportionality held and absolute zero remained the same as the original empirical constant.

Just curious about how this proportionality could have been broken. The specific heat capacity does change with temperature meaning that the relationship is not linear. Also, in the picture below from my first post, the relationship between volume and temperature doesn't make much sense once liquefaction takes place. The first liquefaction of gas took place in 1784 as is quoted at the bottom. How the scientists of those days modify their picture of linear proportionality between temperature and volume/pressure since it could have become clear to them that volume cannot go to zero. I think for a solid once solidification has taken place the pressure could be taken to be zero. Perhaps, they switched to temperature and pressure relationship them. Could you please help me with it?

In the experimental realm, in 1784 Monge achieved, in collaboration with Clouet, the first liquefaction of, a gas, sulfurous anhydride (sulfur dioxide).

Source: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/monge-gaspard

 

[Baluncore]

Just curious about how this proportionality could have been broken. The specific heat capacity does change with temperature meaning that the relationship is not linear.

We are considering volume is dependent on temperature. It can be slightly curved, wobbly and approximate. The gas volume = 0 intercept, will be absolute zero.
You must forgo 20:20 hindsight before reading and understanding the history of science.

Also, in the picture below from my first post, the relationship between volume and temperature doesn't make much sense once liquefaction takes place.

Obviously not. Solids and liquids do not follow the gas laws. You must experiment on progressively lower temperature gases. Helium is solid below 0.95 K, it boils at 4.22 K. That is close enough to absolute zero to avoid most non-linearities. All you need is a cryogenic refrigerator that uses He as the working fluid.

There is a parallel to the gas laws in the search for absolute zero. The resistance of solid metallic elements intercepts zero resistance at absolute zero temperature. Many metals become superconductors at low temperatures. The tungsten critical temperature is about 0.015 K. The noble metals gold, silver and copper do not appear to become superconductors so they can be used as linear cryogenic thermometer elements.