Heating suprecritical water in a closed water tank

Question

How does the pressure of water in a closed tank evolve in the following setting: - closed tank of 2 liters (filled up with water) - water initially at 25°C and pressurized to 3 bars

The water is now heated up to 130°C, thus remaining a fluid (based on water property tables). The specific volume of water increases roughly by 6% due to the temperature increase. Since the water is in a closed tank, it cannot expand, thus the pressure needs to increase.

Which equation will allow me to calculate the resulting pressure in the water tank?

Thanks in advance for any hints and help

Answer 1

For water, the equation of state is semi-empirical and so the choice depends on how accurate you want to be and the range of temperature/pressure/etc that you're interested in.

Equation 19 in Jeffery et al [1], where the parameters are given in equation 32, seems appropriate.

[1] Jeffery, C. A., and P. H. Austin. "A new analytic equation of state for liquid water." The Journal of chemical physics 110.1 (1999): 484-496. Direct PDF link here.

Answer 2

Fluid reserved in a fixed volume and with no inlet and outlet of mass variations are represented well by a parameter called internal energy, although, it does not variates expressive by the pressure, but it does from the temperature. It is an important parameter to systems like yours.

I usualy use a software that does the calculations for me, so i have good precision and i dont need to keep consulting the termodinamical tables. https://www.irc.wisc.edu/properties/

As if you know the variation of the specific volume, you can enter the 25C and 3bar for pressure and get the spec. volume. Then, use your variation of 6% to increment it... now you can enter the 130C as temperature and the specific volume to calculate the pressure you want :)