An ideal gas enclosed in a vertucal cylindrical
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helium is one such example of gas
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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 V0V0 and its pressure is P0P0. 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 :
(1)12πAγP0V0M(2)12πV0MP0A2γ(3)12πA2γP0MV0−−−−−√(4)12πMV0AγP0−−−−√(1)12πAγP0V0M(2)12πV0MP0A2γ(3)12πA2γP0MV0(4)12πMV0AγP0
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A)
Solution :
As adiabatic process
PVγPVγ = Constant
dpp+γdvvdpp+γdvv=0=0
dp=−PγV
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