How Do You Find and Prove a Critical Point in Thermodynamics?

[Spoolx]

1. Find Critical Point and Prove it



2. dP/dV =0



3. n/a

Hey guys, so our professor was talking about critical points in class. He mentioned on our exam we would have to find a critical point and prove it.

Anyhow none of our homework problems ask this, and very little info in the book demonstrates this.

I am not asking for a specific question but basically how would I go about solving a problem like this? I know the critical constants are in the Thermodynamic Tables.
But if my professor asked for the critical points I would go to those tables, not sure how I would calculate them or prove them.

Any help is appreciated (I apologize if this is in the wrong forum)

Thanks

 

[jambaugh]

As far as proofs go, I would start with the definition he gave of a critical point. You then need to show the situation satisfies the definition. Beyond that you've given very little to go on. What are you given from which to prove/find a CP?

 

[Spoolx]

Thats the thing, he really never said.

His exact words were.
"On your midterm you will be expected to find the critical point and prove it"

In the lecture notes he only mentions dP/dV = 0

In the book it mentions very little about the critical point and tells us to use the tables to find it.

I foresee his question being (although I am just guessing, this is what I am expecting.)

"Find the critical point of water, and prove it"

 

[jambaugh]

The critical point is the point beyond which a substance ceases to have a phase transition boundary. I.e. for water beyond a certain pressure and temperature which is its critical point its phase is that of a supercritical fluid where it will no longer transition to a conventional gas under increasing temperature nor to a conventional liquid or solid under increasing pressure.

The distinguishing feature is as you've cited the ability to compress without change in pressure (given fixed temperature), dP/dV=0.

One doesn't prove a critical point but rather observes it. The only "proof" I can imagine is an argument that the definition is satisfied so understand the definition.

Especially look at the definition of a http://en.wikipedia.org/wiki/Supercritical_fluid" .

 

[DeeNos]

for the question! A critical point in thermodynamics refers to the point at which a substance undergoes a phase transition, such as from a liquid to a gas. At this point, the temperature and pressure of the substance are at their critical values, and any further changes in temperature or pressure would result in a change in the phase of the substance. In order to find the critical point, you would need to use the thermodynamic tables to determine the critical temperature and pressure for a specific substance. The critical temperature is the temperature at which the substance transitions from a gas to a liquid, and the critical pressure is the pressure at which this transition occurs.

To prove the existence of a critical point, you can use the Clausius-Clapeyron equation, which relates the change in temperature and pressure at a phase transition. By setting the derivative of this equation to zero, you can find the critical point where the slope of the curve is equal to zero, indicating a phase transition. This is represented by the equation dP/dT = 0.

I hope this helps in understanding how to find and prove the existence of a critical point in thermodynamics. Good luck on your exam!