# A thermodynamics problem

1. Aug 3, 2010

### kagnaroos

1. The problem statement, all variables and given/known data

[PLAIN]http://img101.imageshack.us/img101/7498/thermo.jpg [Broken]

A cylinder is closed by a massless piston of cross sectional area A which is connected to a spring of constant k. With the spring relaxed, the cylinder is filled with a gas. The initial pressure, volume and temperature are Pi Vi and Ti. How high will the piston rise if its temperature is increased to a final value of Tf?

2. Relevant equations

3. The attempt at a solution

I tried to find Pf and Vf.

Pf = Pi + kx/A
Vf = Vi + Ax

I then wrote the universal gas law for Pf Tf and Vf but I doubt this is correct because the equation was crazy long and complicated.

Last edited by a moderator: May 4, 2017
2. Aug 3, 2010

### ehild

In spite of being crazy long ad complicated, it might be correct. There were no numerical data?

ehild

3. Aug 3, 2010

### kagnaroos

Nope, only letters. Are the expressions I wrote for Pf and Vf correct?

4. Aug 3, 2010

### Andrew Mason

You have written out the expression for the pressure as a function of x and volume as a function of x. All you have to do is relate that, using the ideal gas law, to the change in temperature.

AM

5. Aug 3, 2010

### ehild

I think they are correct. But the expression for x will be really ugly. Just go ahead.

ehild

6. Aug 3, 2010

### kagnaroos

kx2 + (PiA + kVf/A)x + nR(Ti-Tf) = 0

I highly doubt this is the correct answer because this is an old exam question and impossible to do in ~10 minutes.

7. Aug 3, 2010

### ehild

Well, it is not quite correct, there should be Vi instead of Vf in your term kVf/A. And you should replace nR by piVi/Ti.

Then use the formula for the solution of quadratic equations and exclude the negative root. It takes less time than 20 s.

ehild