How to get critical temperature from experiment?

Outrageous

Besides plotting P-V graphs,then see the graph shape.
Do we have any other way to get the value of critical temperature of a substance?

Thank you.

Chestermiller

What is your understanding of the definition of the critical temperature? This should help you identify a method.

Outrageous

Critical temperature of a substance is the temperature which the vapour of the substance cannot be liquefied no matter how high pressure applied to the vapour.
So I should keep the volume constant and then heat the liquid inside the fixed volume until at a temperature ,there will no more liquid? Then at that pressure will be the critical pressure.

K^2

There is nothing really special about critical temperature at any given pressure.* So I don't think there is a direct experiment to look for critical temperature. You can, however, look for critical point which will give you both critical temperature and critical pressure. You do this by following along the transition point until the latent heat of transition goes to zero.

For example, you can use a constant pressure calorimeter, supply heat at steady rate and track temperature change. Look for the place where temperature temporarily levels out - that's your transition temperature. Increase pressure and repeat. The plateau will now have narrower range in energy. Keep increasing pressure until that plateau disappears. That's your critical point.


* Edit: Actually, there is an estimate you can make based on surface tension and Eotvos rule. Surface tension at critical temperature does go to zero, so I guess, I shouldn't say that there is nothing special. I suspect, it's very difficult to measure the surface tension near the critical point, but you should be able to at least extrapolate the approximate critical temperature by taking measurements at different temperatures. If nothing else, this will tell you where to look for critical point in finer detail.

Chestermiller

That could work, but you have to be sure that you have enough liquid fraction initially within the container so that all the liquid doesn't evaporate before you reach the critical temperature. Completely filling the container initially should do the trick, but you should do some calculations for various liquids of known VLE and PVT (vapor) behavior to make sure that that is the case.

You can also use the definition. Start our with vapor in a container at a fixed temperature, and increase the pressure isothermally until liquid (fog) starts to form. If it does, start again at a higher temperature. Keep increasing the temperature until liquid no longer forms no matter how high the pressure.

Outrageous

What are VLE and PVT?

Chestermiller

VLE stands for vapor-liquid equilibrium (saturation pressure vs saturation temperature). PVT stands for pressure, volume, temperature behavior; in this case, I meant it to mean the PVT behavior of the vapor.