An ideal gas is contained in a large jar of volume V 0 . Fitted to the jar is a glass tube of cross-sectional area A in which a metal ball of mass M fits snugly. The equilibrium pressure in the jar is slightly higher than atmospheric pressure p 0 because of the weight of the ball. If the ball is displaced slightly from equilibrium it will execute simple harmonic motion (neglecting friction). If the states of the gas represent a quasistatic adiabatic process and γ is the ratio of specific heats, find a relation between the oscillation frequency f and the variables of the problem.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Assume the pressure in the jar is p. As the process is adiabatic, we have
pV γ = const,
giving
+ γ 
= 0.
This can be written as F = Adp = – kx, where F is the force on the ball, x = dV/A and k = γ A 2 p/V. Noting that p = p 0 + mg/A, we obtain
F = 
= 
= 
.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems