Ideal Gas and Spring

Hi there,

I have a problem that I believe I am doing correctly, but my answer proves otherwise. I was hoping someone could take a look and let me know where I'm going wrong.

Here's the problem: A gas fills the right portion of a horizontal cylinder whose radius is 5.10cm. The initial pressure of the gas is 1.01x10^5 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.0cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

So here's what I've done. The final equation that I'm going to need to get to is the ole F = kx equation. And since the length doubles it would probably look something like F = k[2(x)]

But alas I'm missing F and I believe x after converting to meters would be 0.180m.

So I have a Pressure and radius. With the radius I found the area using A = (pie)r^2

Now I have an Area.

From there I used the equation P = F/A to find F. And once getting F I went back to my initial equation plugging in F and solving for k. But my answer is not correct. I was almost sure this was how to solve this problem, but I guess not.

Any help would be greatly appreciated.

Energy stored in the spring after it is compressed to a distance x is

$$\frac{1}{2}kx^2$$

This is equal to the work done on it by the gas due to its expansion. So, to calculate the work done by the gas, use the equation for work done by the gas in an isothermal expansion.

$$W=nRTln\frac{v_f}{v_i}$$

where $$nRT=p_iV_i$$
Hope that helps!

spacetime
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