Understanding Work Calculation for Gray Tin Transformation to White Tin

[RPI_Quantum]

This is a thermodynamical question:

If Gray tin is isothermally transformed to white tin, how would the work done be calculated? The pressure obviously changes, and the densities can be looked up. But I have no idea how to attack this beyond that.

 

[Bystander]

"The pressure obviously changes" is based on what information given in the original problem statement?

How is mechanical work calculated? Calculate this work the same way, integrate PdV.

 

[RPI_Quantum]

Well I know that I should integrate PdV. All that is given in the problem is that white tin transforms to gray tin at a constant temperature of 25 C. The densities of gray and white are the only additional information provided.

I do not know the expression for P to integrate.

 

[Bystander]

You walk into the lab. You set up an experiment on the bench, in the hood, or elsewhere. You heat things, you cool things, you boil them in molten salt and quench them in boiling oil. How often do you have to wear a pressure suit, or climb into a diving bell to do the work?

One atmosphere do ya?

The problem statement says "isothermal." You've been taken through the Gibbs Phase Rule? Degrees of freedom equals number of components (one, Sn), minus number of phases (two, white and grey), plus two; you have one degree of freedom, temperature, and it's been fixed with the isothermal statement. P has to be constant, or you've moved the transition temperature.

Hitting you with a problem like this without GPR first is asking a bit much.

 

[RPI_Quantum]

Yeah, okay I'm an idiot... Of course I've seen the phase rule, I just was not looking at the problem carefully. I guess that somewhere in the back of my head I was thinking constant pressure made this too simple of a problem.

Thanks for allowing me to realize my stupidity.

 

[Bystander]

Don't flog yourself. If that's the biggest mistake you ever make in your life, you will have set a new record high score in the human endeavor to achieve perfection.

 

[RPI_Quantum]

Of course! I will just laugh at myself in this situation and look back on it when I am 3/4 through this semester of advance thermo. It's just funny that I chose to mess up the easy stuff. I think it is a habit with me!

 

[Astronuc]

Just a little background from Webelements -

Ordinary tin is a silvery-white metal, is malleable, somewhat ductile, and has a highly crystalline structure. Due to the breaking of these crystals, a "tin cry" is heard when a bar is bent. The element has two allotropic forms. On warming, grey, or a-tin, with a cubic structure, changes at 13.2°C into white, or b-tin, the ordinary form of the metal. White tin has a tetragonal structure. When tin is cooled below 13.2°C, it changes slowly from white to grey. This change is affected by impurities such as aluminium and zinc, and can be prevented by small additions of antimony or bismuth.