Simple Applications of Macroscopic Thermodynamics

[vladittude0583]

Homework Statement

The following describes a method used to measure the specific heat ratio "gamma" of a gas. The gas, assumed ideal, is confined within a vertical cylindrical container and supports a freely moving piston of mass m. The piston and cylinder both same the same cross-sectional area A. Atmospheric pressue is p₀, and when the piston is in equilibrium under the influence of gravity (acceleration g) and the gas pressure, the volume of the gas is V₀. The piston is now displaced slightly from its equilibrium position and is found to oscillate about this position with frequency "nu." The oscillations of the piston are slow enough that the gas always remains in internal equilibrium, but fast enough that the gas cannot exchange heat with the outside. The variations in gas pressure and volume are thus adiabatic. Express "gamma" in terms of m, g, A, p₀, V₀, and "nu"

Homework Equations

pV^(gamma)=constant.

The Attempt at a Solution

1) Since the gas cannot exchange heat with the outside, then I know that Q = 0 right?
2) When the piston is in equilibrium under "g" and the gas pressure, the force from the gas has to exactly balance out the gravitational force due to the piston right?
3) Do I have to take into consideration of potential energy in terms of oscillatory motion?
4) Since Q = 0, then we know that the change in energy is equal to the work done right?
5) Any advice towards the correct direction to solving this problem would be greatly appreciated.
6) Thanks!

 

[Mapes]

5) Any advice towards the correct direction to solving this problem would be greatly appreciated.

Sinusoidal oscillations generally occur when there's a restoring force that increases with displacement. In this case, the pressure increases slightly when the volume decreases due to the piston moving downwards, and this causes the piston to rebound. You'll probably want to look into the relationship between this restoring force and the frequency of oscillation.