I'm currently doing an investigation for school on finding the Clausius-Clapeyron relation/gradient for boiling water and comparing it to the gradients along my line of best fit. It is given by the equation, $$ \frac{\text{d}P}{\text{d}T} = \frac{L}{T\Delta v}. $$ I'm having trouble finding the specific volume of both water and steam (I found this for water but I'm not sure of the credibility) for $\Delta v$. I was hoping someone could reference me to a large data table for finding the specific volume, or a calculator. Thank you.
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1$\begingroup$ For every constant related to chemistry and physics, I would advise the "CRC Handbook of Chemistry and Physics". At least it was everywhere before the internet changed the whole game. But it does not make it useless. $\endgroup$– SteffXCommented Mar 14, 2019 at 15:19
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$\begingroup$ Thank you I'll check it out, I believe we have one at school but since I have a large table of data I was hoping I could just copy paste. If worst comes to worst this will be fine. $\endgroup$– John MillerCommented Mar 14, 2019 at 16:48
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$\begingroup$ @JohnMiller When I had vaguely-similar lab assignments in university, they directed us to an online (pay-walled) version of the CRC Handbook. Tables were mostly copy-able, though not always with the best formatting. $\endgroup$– mbrigCommented Mar 14, 2019 at 21:42
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2 Answers
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Such values for various properties of liquid water and steam can be looked up in so-called steam tables. Software versions also allow calculations (ususally interpolation) of additional values. For example, I usually use REFPROP – NIST Standard Reference Database (however, not always the latest version) or some old and simple proprietary steam table software from Siemens/KWU.
If you do not have access to professional steam tables, you may want to consider using the steam tables that are included in WolframAlpha.
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$\begingroup$ I was once looking for these and typed "steam tables" into a search engine. I got lots of hits for restaurant equipement. $\endgroup$ Commented Mar 14, 2019 at 18:52
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The usual reference for phase change information, for various substances, is Perry's Chemical Engineers' HandBook by Perry and Green. Then there are the CRC HandBooks and sometimes such information can be gleaned from the Chemical Engineering Encyclopedias (I forget their names now). Then IUPAC, NIST and some other governemntal institutions make such information available. At one point some of the publishers were touting dataset API's though these were/are behind pay walls so you'll have to go through your School/Universities/Local libraries subscription to get the data.
Most of the properties reported within Perry's Chemical Engineers' HandBook originally appeared in two papers
- "Inorganic Compounds (Vapor Pressure of Pure Substances)" appearing in Industrial and Engineering Chemistry 1947 Vol. 39 No. 4 pages 540-550
"Vapor Pressure of Pure Substances" by Daniel R. Stull appearing in Industrial and Engineering Chemistry 1947 Vol. 39 No. 4 pages 517-540 Specifically for water there are the "Steam Tables". I know of two versions
"Steam Tables : Thermodynamic Properties of Water including vapor, Liquid, and Solid Phases" by Joseph H. Keenan, Frederick G.Keyes, Philip G. Hill and Joan G. Moore (ISBN : 0-4710-4210-2)
- "Thermophysical Properties of Water Substance" by Jeffery R. Cooper and Edwin J. Le Fevre (ISBN : 0-7131-3222-1)
Using the latter we have the following information for the triple point :
T(K) P(MPa) Phase *v*(m^3/Mg) *e*(kJ/kg) *h* (kJ/kg) *s*(kJ/(kg K))
------ ---------- -------- ----------- ---------- ----------- --------------
Solid 1.091 -333.5 -333.5 -1.221
273.16 0.0006112 Liquid 1.0002 0 0.0006113 0
Gas 206180 2375 2501 9.156
You can use these values for checking the authenticity of other sources. Also good luck fitting Clausius-Clapeyron the equation is quite sensitive to the constants. I think it was easier to fit on a log curve, or by inverting it If I remember correctly. FSolve in Excel should handle the fitting alright though otherwise matlab, wolfram and pandas/numpy/scipy provide algorithms for the task.
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$\begingroup$ Yeah I've just finished compiling the data in MATLAB and the errors become as big as 60%, but it's what I want as for my IA (the piece of work we need to do) it's good to have errors as you can talk about what you could of done better in hindsight. Thanks for the advice. $\endgroup$ Commented Mar 16, 2019 at 21:17