thermodynamics and gas law problem

[kmwong]

Hi guys so this is the problem I want to ask.

 

For part A I got F=mg +k (deltax),

And for part B I got P=Patm+F/A (F is from part A.)

 

So part C is where I got confused. What does it mean by here quadratic equation? In my mind if the piston is allowed to reach equilibrium, the volume of the gas would change(in this case, double) and the pressure would maintain the same. But them I saw part D part E and so on and I got threw off. I have no idea how to approach part c. Please help!

[studiot]

You have missed a term that adds to the downward force in part A

 

For part B you have added an unecessary term.

 

Why do do think the volume of gas would double?

What law, under what conditions says that?

 

Understanding why this is not so is the key to part C

[kmwong]

I see, so the missing force component for force should be the force by atmospheric pressure right?

[studiot]

Yes the atmospheric pressure exerts a force on th top of the piston.

 

You say the piston is in equilibrium.

 

so parts A and B are not really thermodynamics at all, just basic mechanics.

 

Think of the piston as a free body diagram and balance the vertical forces.

 

Remember that the pressure inside the cylinder is absolute not gauge.

 

Now how about answering my question on C?

[kmwong]

You're right, I don't think any law states that. It's just me getting caught in chemistry calculations where usually only one variable changes...

[studiot]

 

You're right, I don't think any law states that. It's just me getting caught in chemistry calculations where usually only one variable changes...

 

 

Well I was trying to hold a conversation to help you along your journey, but the time gaps were rather large.

 

Do you see that to complete this question you need to calculate both the first law work and heat changes?

 

You also need the fact that one version of the universal gas law is that the internal energy of a perfect gas depends only on temperature.

 

You need to combine the first law with the gas law and your mechanical balance from parts A and B to form a single equation to complete the rest of the problem.

 

Note in setting up the mechanical force balance to choose a consistent sign convention for up and down (have you done this ?)

 

If this is too late, good luck with your submission.