# Water Thermodynamic Properties

Syeilendra Pramuditya, Water Thermodynamic Properties, ITB Physics Department – Technical Document, http://portal.fi.itb.ac.id/tecdoc/waterprop

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There are many empirical and analytical correlations have been developed for thermodynamic properties of water. These correlations generally can be found from scientific papers as well as text books.

Correlations presented in this article are polynomial fit to data obtained from XSteam library for Matlab. XSteam itself is a kind of digital library of water properties based on the International Association for Properties of Water and Steam Industrial Formulation 1997 (IAPWS IF-97). These polynomial correlations are meant to be used in computer codes, and they are valid under the following conditions: $p=\textrm{1 bar}$ $5\;C \leq T \leq 95\;C$

or equivalently: $278.15\;K \leq T \leq 368.15\;K$

Water density as a function of temperature (p = 1 bar) Polynomial fit: $\rho(T)={1001.1-0.0867T-0.0035T^2}$ (T in Celcius, unit is kg/m3) $\rho(T)={765.33+1.8142T-0.0035T^2}$ (T in Kelvin, unit is kg/m3)

Water specific heat capacity as a function of temperature (p = 1 bar) Polynomial fit: $C_p(T)={4.214-2.286\times10^{-3}T+4.991\times10^{-5}T^2-4.519\times10^{-7}T^3+1.857\times10^{-9}T^4}$ (T in Celcius, unit is kJ/kg.C) $C_p(T)={28.07-0.2817T+1.25\times10^{-3}T^2-2.48\times10^{-6}T^3+1.857\times10^{-9}T^4}$ (T in Kelvin, unit is kJ/kg.K)

Water thermal conductivity as a function of temperature (p = 1 bar) Polynomial fit: $k(T)={0.5636+1.946\times10^{-3}T-8.151\times10^{-6}T^2}$ (T in Celcius, unit is W/m.C) $k(T)={-0.5752+6.397\times10^{-3}T-8.151\times10^{-6}T^2}$ (T in Kelvin, unit is W/m.K)

Water dynamic viscosity as a function of temperature (p = 1 bar) Polynomial fit: $\mu(T)={1.684\times10^{-3}-4.264\times10^{-5}T+5.062\times10^{-7}T^2-2.244\times10^{-9}T^3}$ (T in Celcius, unit is Pa.s) $\mu(T)={9.67\times10^{-2}-8.207\times10^{-4}T+2.344\times10^{-6}T^2-2.244\times10^{-9}T^3}$ (T in Kelvin, unit is Pa.s)

Water volumetric thermal expansion coefficient as a function of temperature (p = 1 bar)

The volumetric thermal expansion coefficient is evaluated from the density equation, as described in this article.

Polynomial fit: $\beta(T)=7.957\times10^{-5}+7.315\times10^{-6}T$ (T in Celcius, unit is /C) $\beta(T)=-1.908\times10^{-3}+7.318\times10^{-6}T$ (T in Kelvin, unit is /K) ## 10 thoughts on “Water Thermodynamic Properties”

1. theanphibian (@theanphibian) says:

I’m sure this will be useful to someone. That’s cool of you to post it.

Syeilendra said..
Glad to know that my post might be useful to somebody, thanks! 🙂

1. Paulo says:

And so it was… so useful to me. Thanks Syeilendra

Syeilendra said..

2. Unknown says:

what are your references for these equations?

Syeilendra said..
it’s clearly written there >> Correlations presented in this article are polynomial fit to data obtained from XSteam library for Matlab. XSteam itself is a kind of digital library of water properties based on the International Association for Properties of Water and Steam Industrial Formulation 1997 (IAPWS IF-97).

2. sauarav says:

can u tell me wat realtion v shud use if p=1atm

Syeilendra said..
You can use the equations shown in this post, since 1 atm approximately equals to 1 bar.

3. Fred Jones says:

Very useful to me, thanks for posting! ( I am an amateur winemaker and I wanted to know how much wine would expand and contract in volume with changes in temperature within a certain range.)

Syeilendra said..
Good to know it is useful, you welcome.

4. JOE Wong says:

When I use the above equation to calculate the water specific heat capacity in 5C and 278.15K, the result is difference which is 4.2038 and 4.1709. The difference is significant. How do you get the function?

Syeilendra said..
The more accurate are the Celcius ones. I get the equations by curve fitting from the original XSteam library.

1. JOE Wong says:

Thank you. I will use the Celcius ones. it is useful.

5. R K Pal says:

Dear Sir, I’m doing the simulation of flow boiling, in my system the operating pressure is 45 bar at which saturation temperature of water is 530 K. The inlet water temperature is 473 K. I have to use properties of water liquid as function of temperature. Can you help me regarding this

6. d.pugliesi says:

The units of measure for specific heat in the diagram are wrong. It has to be written “kJ” instead of “J”.

7. Dotan says:

Thanks for this review, really helpful.
It seems that in the graph titled “Water specific heat capacity as a function of temperature (p = 1 bar)”, the y-axis units are incorrect. It says J/kg x C, and I think it should be kJ per kg, as is written in the equation under the figure.

Thanks again!