How high will the piston rise if its temperature is increased?

[kagnaroos]

Homework Statement

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

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 P_i V_i and T_i. How high will the piston rise if its temperature is increased to a final value of T_f?

Homework Equations

The Attempt at a Solution

I tried to find P_f and V_f.

P_f = P_i + kx/A
V_f = V_i + Ax

I then wrote the universal gas law for P_f T_f and V_f but I doubt this is correct because the equation was crazy long and complicated.

 

[ehild]

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

ehild

 

[kagnaroos]

Nope, only letters. Are the expressions I wrote for P_f and V_f correct?

 

[Andrew Mason]

...

I then wrote the universal gas law for P_f T_f and V_f but I doubt this is correct because the equation was crazy long and complicated.

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

 

[ehild]

Nope, only letters. Are the expressions I wrote for P_f and V_f correct?

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

ehild

 

[kagnaroos]

That gives a quadratic equation:

kx² + (P_iA + kV_f/A)x + nR(T_i-T_f) = 0

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

 

[ehild]

Well, it is not quite correct, there should be V_i instead of V_f in your term kV_f/A. And you should replace nR by p_iV_i/T_i.

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

ehild