Source
r/AskPhysics•
__August

Absolute Zero and Interpolation

I am currently studying Thermodynamics from MIT OpenCourseWare. While teaching about the ideal gas law, the professor told that in order to formulate the law, we have to take note of the reference points (those being freezing and boiling point of water). Now after that, we can choose to either do a linear interpolation or a quadratic interpolation (the graph being PV vs T) between the points (I guess to form the equation). When we do the linear one, it results in the discovery of Absolute Zero (x-intercept = 0) as at that temperature PV = 0 (which is not possible). My question is that if both linear and quadratic interpolations are viable, would doing the latter one still result in Absolute Zero (the professor said something along the lines of the x intercept going to infinity but didn't really dive into it that much). Someone else pointed out in the comments that- "Of course, the interpolation curve is not arbitray because it expresses the energy of the system, which is linear in temperature and never can be negative."

It will be really helpful if you can provide some insight regarding this.

Posted Sep 1, 2023, 8:54 PM UTC

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ChemomechanicsMaterials science•

The comment’s incorrect; energy has no absolute reference zero, and we can certainly work with negative energies relative to some arbitrary reference. (We do this all the time with gravitational and electrostatic energies, for example, which are often negative because the reference is set to infinite distance.) For the ideal gas, we happen to often take the reference zero as absolute zero on the temperature scale, but this isn’t required.

You can interpolate with any function you like, but the simplest is a line. It’s hard to say more without seeing the material you’re asking about.

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__AugustOP•

Blud was waffling then. Thanks for clarifying

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ChemomechanicsMaterials science•

Any time. I wrote a note about the internal energy of the ideal gas—and an aspect that absolutely confuses and frustrates many new practitioners—that you might find useful.

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__AugustOP•

Thanks for that. Haven't really reached internal energy yet but will definitely use it when I do. Thanks again

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starkeffectEducation and outreach•

I've never heard of doing a quadratic fit like that, but it wouldn't be possible with only two points. An infinite number of parabolas will pass through those two points-- you need three points to specify a unique parabola.

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SkirtEfficient1069•

You can add a third point. And problem solved.

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__AugustOP•

That's true. I don't know why I didn't think of that. Thanks

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db0606•

They use a linear interpolation because if you take a bunch of data of PV vs. T, the data look pretty linear (see Fig. 1.3 in Schroeder's Thermal Physics). If you tried fitting a parabola to the data, the fit would look pretty crappy (or the quadratic term would be almost zero). You could do this completely experimentally without appealing to theory. Separately, one can derive from kinetic theory that the energy of an ideal gas is linear in temperature and always positive because in the calculation you are essentially computing the kinetic energy of the gas, which is strictly positive if you use the normal definition. As u/Chemomechanics pointed out, energy in general need not be positive and is only really defined up to a constant, which doesn't really matter since we only ever really deal with differences in energy, when analyzing the behavior of physical systems.

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__AugustOP•

Thanks. I get it now

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