John Carlos Baez

I'm trying to calculate the entropy of hydrogen and helium and compare these to experiment. The National Institute of Standard and Technology lists these entropies here:

https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Mask=1#Thermo-Gas

https://webbook.nist.gov/cgi/cbook.cgi?ID=C7440597&Mask=1#Thermo-Gas

But unfortunately it doesn't say at what temperature! I need accurate figures at any clearly specified temperature and pressure. Can you help?

The back story:

Wikipedia says that NIST says "standard temperature and pressure" is 20 °C and 1 atmosphere (101.325 kilopascals). But the book Modern Thermodynamics with Statistical Mechanics by Carl S. Helrich says something completely different: it claims the NIST standard is 25 °C and 1 bar (100 kilopascals).

The actual NIST webpages above say the entropies are measured at 1 bar, but they don't say what temperature they are using! Nor is it easy to find a page where they answer that question. You might think their FAQ would do that, but it doesn't. It only has helpful comments like this:

Q: Can you help me with my homework?

A: No.

[Addendum: if you read on, you'll see the solution to this problem is truly shocking.]

Hydrogen

Jun 28, 2024 at 2:39pmWeb
Show threadDougMerritt (log😅 = 💧log😄)Jun 28, 2024

@johncarlosbaez Should be standard temperature and pressure, 0 °C 1 bar

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

Standard temperature and pressure - Wikipedia

Show threadJohn Carlos BaezJun 28, 2024

@dougmerritt - I mentioned what Wikipedia said about this: it claims NISTs version is 20 C and 1 atmosphere, which is different from what you just said.

I then mentioned a chemistry book that said something else - neither what you said nor what Wikipedia says!

Given this cloud of confusion, what I'd really like is something from NIST. Their FAQ doesn't have it, nor does their "guide":

https://webbook.nist.gov/chemistry/guide/

A Guide to the NIST Chemistry WebBook

Show threadDougMerritt (log😅 = 💧log😄)Jun 28, 2024
@johncarlosbaez I misread, sorry for being unhelpful.
Show threadJohn Carlos BaezJun 28, 2024

@dougmerritt - no prob; turns out the solution is to view NIST's database on my cell phone, and *then* I can see that the entropy of helium is being measured at 25 C, 1 bar - not at 20 C, 1 atmosphere like Wikipedia claims, and not at 0 C, 1 bar like you claimed.

(Yes, sadly, 1 bar ≠ 1 atmosphere.)

"Standard temperature and pressure" is one of those things that make people say "the great thing about standards is how many of them there are."

Show threadAndrocatJun 28, 2024

@dougmerritt @johncarlosbaez

Wow. Vaguery and pernicious standarding afoot.

Show threadpounce  Jun 28, 2024

@johncarlosbaez
when you view the website on mobile it very clearly displays the temperature (25°C) and pressure (1 bar) which seems to vanish in desktop mode.

not sure if this helps.

Show threadJohn Carlos BaezJun 28, 2024

@pounce - wow, that's great! Thanks! Here is what I'm seeing on my desktop on that same page:

https://webbook.nist.gov/cgi/cbook.cgi?ID=C7440597&Mask=1#Notes

The temperature is not visible! I never dreamt I'd have to switch to my mobile phone to find out what temperature the entropy of helium was measured at! 😵

helium

Show threadj5vJun 28, 2024
@johncarlosbaez
Kudos for not just assuming [whatever standard you might have seen many years ago]
Show threadJohn Carlos BaezJun 28, 2024
@j5v - I've been having a lot of trouble with my calculations, and I woke up last night and realize *some* of them may be due to using the wrong "standard temperature".
Show threadBenMonrealJun 28, 2024
@johncarlosbaez every WebBook data entry has a literature reference. Looks like the hydrogen entropy cites CODATA, and the PDF someone has uploaded here (which agrees with the NIST H2 value) specifies 298.15K https://www.science.co.il/chemistry/databases/Codata-key-values-for-thermodynamics.pdf
Show threadJohn Carlos BaezJun 28, 2024
@BenMonreal - thanks! This agrees with what someone else pointed out: namely, you can see what temperature NIST is using if you view the page using your cell phone, not your desktop. 😵
Show threadChristopherJun 28, 2024
@johncarlosbaez I recall when I did A level chemistry at school, STP was 1 atmosphere/bar (the difference between the two was beyond A level accuracy) and 298 K (i.e. 25 C - we could also ignore the odd 0.15 K for the same reason). Our teacher commented that this was a change from 20 C which had been the British standard "because American laboratories are hotter". I can't vouch for the accuracy of that, but one day it was remarked that the laboratory was actually at 298 K, or as we described it, too hot.
Show threadJohn Carlos BaezJun 28, 2024

@dearlove - as it turns out, the National Institute of Standards and Technology data on the entropy of hydrogen and helium were listed for 1 bar and 298.15 K. So it's basically what you had for A level chemistry. But I'm worrying about fine details so I decided to worry about the odd 0.15 K, etc.

In fact now that I've got this straightened out, my theoretical calculation of the entropy of helium is only 1.4% below what NIST says! That's fine because I'm leaving out most quantum mechanical effects.

I have a student @Joemoeller who worked at NIST, and he can confirm that it gets hot in the summer there... at least outside: it's air-conditioned.