Read also this: Liquid Sodium Thermodynamic and Transport Properties
The volumetric thermal expansion coefficient of Sodium is around 0.0002 /K, it depends on temperature and pressure, and the following is a brief description.
Some Liquid Metal-cooled Fast Reactor (LMR) designs employ Sodium as coolant material in its primary heat transport system. And one of the important physical properties of Sodium used in thermal hydraulic analysis is the volumetric thermal expansion coefficient (usually denoted by the Greek letter Beta).
Beta is expressed as follow:
By using the above formula, we can now evaluate if we know the dependency of density on temperature. This dependency is available in form of tabular data or empirical correlations. I will use the following correlation, which I obtained from a reliable source:
So by using the above empirical formula, now you can easily evaluate the value of at any “valid” temperature and pressure.
As an example, here is the plot of as a function of temperature, keeping the pressure constant at 101325 Pa (equal to 1 atm):
We can see that the relation between and temperature “looks” linear, so for pressure value of 1 atm, can be approximated by the following simplified equation:
So how accurate this formula is?
Well, Wikipedia says that the relation between volumetric and linear thermal expansion coefficient can be approximated as , and this link and this link say that the linear coefficient is around , which implies that the volumetric coefficient should be around 3 times of that value, or about . And this link says that the value is .
So the above formula is quite good, I think.
- Reading material from KTH
- Liquid Sodium Thermodynamic and Transport Properties
- Water thermodynamic properties (in polynomials) at pressure of 155 bar (typical PWR operating condition)