Randall D. Knight — A Macroscopic Description of Matter: Problem 74

The closed cylinder of FIGURE CP18.74 has a tight-fitting but frictionless piston of mass M. The piston is in equilibrium when the left chamber has pressure p0 and length L0 while the spring on the right is compressed by \Delta L. a. What is \Delta L in terms of p0, L0, A, M, and k? b. Suppose the piston is moved a small distance x to the right. Find an expression for the net force (Fx)net on the piston. Assume all motions are slow enough for the gas to remain at the same temperature as its surroundings. c. If released, the piston will oscillate around the equilibrium position. Assuming x << L0 find an expression for the oscillation period T. Hint: Use the binomial approximation.