How Are Thermodynamic Property Tables Created?

[MotoPayton]

In the back of my thermodynamics book it has large quantities of thermodynamics properties listed for water--ie temperature, pressure, specific volume, internal energy, enthalpy, and enthalpy.

I would like to know how these tables are built and the methods used to ascertain the data in general, not necessarily the specific method for water.

From reading wikipedia, I know that internal energy is zero at zero Kelvin and then it rises with increasing temperature where its value is representative of the sum of kinetic and potential energies of the system. So If I wanted to find the internal energies for water how would I do it? This equation below seems reasonable except how would I find Cv(T) when calculating the integral. Also obtaining zero Kelvin is "impossible" or not easy to do so these values must have been determined some other way. Maybe reaching close to zero and approximating the data at lower temps.. Really curious on this one. I feel like I should understand this for a more complete understanding of thermo.
https://www.google.com/search?q=int...wikipedia.org%2Fwiki%2FInternal_energy;295;51

 

[Simon Bridge]

You can usually work out how to measure specific material properties by their definition.

eg. Zero Kelvin is done by cooling and heating different gasses and plotting the volume against the temperature for the range of values you can achieve (using any temperature scale you like). Observe that these are lines, find the equations of those lines, then solve for temperature given zero volume. This will give you a range of values for absolute zero.

The closer you get to that figure in the experiments, the better the measurement will be, but you don't have to get very close to see the effect. The exact method depends on the equipment to hand - you can use a balloon, calipers, and a thermometer for this experiment, though we'd rather use a constant-volume gas thermometer (look it up).

As you can imagine - these experiments have to be conducted very carefully and they are always being improved. Repeat the details for every property on your list and you'll see the task you have presented to us :)

 

[MotoPayton]

Ok, yes. Put one mole of an inert gas into a constant volume container and measure the pressure at varying temps. If using the atm,mole,celcius,liter system you will find 22.4 liters at 0 celcius and 1atm no matter what. Then you can follow that line all the way to zero pressure and notice that the temperature is -273C. Then shift your axis and you have ideal gas law for kelvin system.
I found some pertinent literature and it explains that property values are not exact or even close to exact. They are assigned zero values at arbitrary locations and then the differences in energy from that state are measured through testing. ie: at .01 degrees C water is given 0 internal energy and 0 entropy. Then someone I guess calculates the internal energy levels and other properties at differing temperatures. From the equation I posted I don't understand the method of retrieving that data. because the change in internal energy in the equation I posted relies on Cv itself which is the change in internal energy wrt temp, it implies you already know a relation between internal energy and temperature. But if your trying to find the values for internal energy you do not have that equation for Cv available to you.
I just want to know how someone would find all these values in practice.

 

[Simon Bridge]

The "zero" value is usually some reference value yes, and all other measures are "with respect to" that reference.
Some choices of reference value make more sense than others.

But all measures are like that - where is the "zero" for position?

Water is a good choice for setting some things to zero because we can measure other things by how they change the water they come into contact with ... which will establish a value for the what you are measuring in comparison with that for water.

Similarly you measure distance by using a standard length - all distances are in comparison to that length.
This is how you get a system of units.

Go back to the definition of internal energy and temperature... and the experimental basis for their relationship.
You should be able to see how to get values for them.

 

[PJC01]

The property tables in your thermodynamics book are most likely built using experimental data and mathematical models. To obtain the data, experiments are conducted at various temperatures and pressures, and the resulting values for specific volume, internal energy, enthalpy, and other properties are recorded. These data points are then used to create mathematical models, such as equations or graphs, that can be used to estimate the properties at any given temperature and pressure within a certain range.

In terms of finding the internal energies for water, the equation you referenced is a reasonable approach. However, as you mentioned, obtaining data at temperatures close to absolute zero is not feasible. In this case, extrapolation techniques may be used to estimate the values at lower temperatures. Additionally, there are also theoretical models and equations based on thermodynamic principles that can be used to calculate the internal energy at any temperature.

Understanding the methods used to determine these properties is important for a complete understanding of thermodynamics. It allows us to accurately predict the behavior of substances under different conditions and make informed decisions in various engineering and scientific applications.