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This question is from Thermal Physics by Ralph Baierlein chapter 1.

Ruchardt's experiment: equilibrium. A large vessel of volume [tex]V_0[/tex] to which is attached a tube of precision bore. The inside radius of the tube is [tex]r_0[/tex], and the tube's length is [tex]l_0[/tex]. You take a stainless steel sphere of radius [tex]r_0[/tex] and lower it sloly-down the tube until the increased air pressure supports the sphere. Assume that no air leaks past the sphere (an assumption that is valid over a reasonable interval of time) and that no energy passes through any walls.

This is what I first did. No energy is passed through the wall, so the system is an adiabatic one. For a adiabatic system

[tex]P_f V^\gamma_f = P_i V_i^\gamma[/tex]

Where

[tex]\gamma = \frac{C_P}{C_V}[/tex]

[tex]V_f = \pi r^2_0 (l_0 - l) + V_0[/tex]

and

[tex]V_i = \pi r^2_0 l_0 + V_0[/tex]

Volume V is the total volume of the tube and the container.

The final pressure is just

[tex]mg/A[/tex]

Where mg is the weight of the sphere and A is the cross-sectional area of the tube.

The problem I'm facing is when I manipulating the equations and solve for [tex]l[/tex], I cannot eliminate the variable [tex]N[/tex] (the number of molecules which arises from the ideal gas law) and the intial and final temperature [tex]T_i[/tex] and [tex]T_f[/tex] which also arises from the ideal gas law.

ie

[tex] P = \frac{N}{V}kT [/tex].

Any help is appreciated

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# Homework Help: A Question on Pressure

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