Finding specific heat C_p coefficients using NIST

[JD_PM]

TL;DR Summary

I am trying to find the specific heat (at constant pressure) $C_p$ coefficients linked to the JANAF model

I am trying to find the specific heat (at constant pressure) $C_p$ coefficients linked to the JANAF model, which basically assumes that $C_p$ is a polynomic function of $T$, for liquid nitrogen (at $\approx$ 97 K).

Before doing that, I am trying to find those for water (at $\approx$ 300 K) and verify that they are $9850.69, -48.6714, 0.13736$ and $-0.000127063$.

I am looking into NIST data for water; I checked both gas and condensed thermochemistry data but the coefficients don't match with the above. I also checked the NIST-JANAF thermo tables, for water, but the coefficients are not there.

How to find the desired coefficients for water (at $\approx$ 300 K)? They should be somewhere in the NIST-JANAF table.

Once I see the above it should be straightforward to find those for liquid nitrogen

Thank you!

PS: Actually, I am implementing the thermo-physical properties of liquid nitrogen.

 

[BvU]

Before doing that, I am trying to find those for water (at $\approx$ 300 K) and verify that they are $9850.69, -48.6714, 0.13736$ and $-0.000127063$.

Where do these come from ? How do they lead to a $\ c_p=75.349\$ J/(K.mol) as expected ?

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[JD_PM]

Just for the record, here's an explanation of the JANAF model

Where do these come from ? How do they lead to a $\ c_p=75.349\$ J/(K.mol) as expected ?

$\$

Good question, here is the derivation.

I am trying to find the coefficients for liquid nitrogen online. However, I think the best I could do is follow the same procedure to derive them (not only for $c_p$ but for the density, dynamic viscosity and thermal conductivity).

So I am going to take the temperature range $-193 < T < -173$ Celsius (using $80K < T < 100K$ should also work).

First I am trying to find the density, $c_p$, dynamic viscosity and thermal conductivity data associated to this temperature range (as done for water in the above derivation).

 

[BvU]

Good question, here is the derivation.

Still think there is a mismatch somewhere. I can find no way to get a reasonable $c_p$ with e.g. formula $(23)$ or $(24)$ with such coefficients $$9850.69*300^4 -48.6714*300^3+ 0.13736*300^2 -0.000127063*300 = 7.979 \times 10^{13}\ \ ?$$

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[DrClaude]

I am looking into NIST data for water; I checked both gas and condensed thermochemistry data but the coefficients don't match with the above.

The NIST data is for the Shomate equation, which is not polynomial (note the $E/t^2$ term).

 

[JD_PM]

Still think there is a mismatch somewhere. I can find no way to get a reasonable $c_p$ with e.g. formula $(23)$ or $(24)$ with such coefficients $$9850.69*300^4 -48.6714*300^3+ 0.13736*300^2 -0.000127063*300 = 7.979 \times 10^{13}\ \ ?$$

$\$

There are no formulas numbered 23 nor 24. Did you mean 7.4 here?

 

[BvU]

Just for the record, here's an explanation of the JANAF model
https://www.physicsforums.com/attachments/298450