An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium,

Question

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$ . The piston and the cylinder have equal cross-sectional area $A$ . When the piston is in equilibrium, the volume of the gas is $V_{0}$ and its pressure is $M_{0}$ . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

TestHub · Accepted Answer

For an adiabatic process, Pv γ = constant Differentiating with respect to v , dP dv v γ + P γ v γ - 1 = 0 dP = - γP v dv = - γP v Adx Thus, the acceleration, a = dF M = γ PA 2 MV dx Comparing with , a = - ω 2 dx , we get, ω = γ P 0 A 2 M V 0 = 2 π f f = 1 2 π γ P 0 A 2 M V 0

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