How High Does the Piston Rise in an Ideal Gas Problem?

[andrew410]

I think this is a ideal gas/ thermal expansion problem.

A cylinder is closed by a piston connected to a spring of constant 2*10^3 N/m. With the spring relaxed, the cylinder is filled with 5 L of gas at a pressure of 1 atm and a temperature of 20 degrees Celsius. a) If the piston has a cross-sectional area of 0.010 m^2 and negligible mass, how high will it rise when the temperature is raised to 250 degrees Celsius? b) What is the pressure of the gas at 250 degrees Celsius?

Use this figure to solve the problem:

[PLAIN]http://east.ilrn.com/graphing/bca/user/appletImage?dbid=2121095896

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I'm not sure where to start with this problem. Any help will be great.
Thanks!

 

[kenhcm]

Assume the height for the piston to rise is h.

The final volume of the gas in the cylinder is V_i+A*h. From idea gas law, you could obtain the expression of the pressure P_f in terms of h.

The final pressure is also given by the expression 1 atm + k*h/A where k is the spring constant and A is the surface area of the piston.

Equate these two expressions of the final pressure, you could solve for the h. Once this has been solved, you could easily determine the final pressure of the gas in the cylinder.


Kenneth

 

[andrew410]

How did you get the formula for final volume and final pressure?

 

[kenhcm]

When the piston has been risen by h, isn't it the volume of the gas has been increased by A*h? Recall that the volume of the cylinder is the surface area times the height.

The final pressure of the gas in the cylinder can be determined from the ideal gas equation: $$\frac{PV}{T}=\hbox{constant}$$. At the condition of the equilibrium, the pressure inside the cylinder is the same as the one outside. The pressure outside is just the sum of the atmospheric pressure and the pressure acting on the piston by the spring. Recall that the pressure is defined by $$P=\frac{F}{A}$$ and the force exerted by the spring is given by $$F=kx$$ where x is the displacement of the spring.


Kenneth

 

[andrew410]

Ahh...I see now...I keep forgetting the basics...
Thank you very much!

 

[andrew410]

The answer I got was incorrect...The equation was:
$$\frac {RT} {V_{i}+Ah} = 101325 - \frac {kh} {A}$$
I solved for h on the calculator and my answer was .502 m.
I changed the temperature to Kelvin and used 8.314 as R.
The mass was negligible so $$n$$ was gone.
Is there something I did wrong?

 

[andrew410]

Could anyone help me? I got to turn the homework in soon.