Q.
A piston of cross-section area A is fitted in cylinder in which gas of volume V at pressure P is enclosed. Gas obeys Boyle's law, what is angular frequency it piston is displaced slightly?
Since, gas obey’s Boyle’s law, so it is isothermal process.
The bulk modulus for gas is given by B=−ΔV/VΔp
But as gas obeys Boyle’s law,so pV= constant (isothermal process)
In isothermal process, isothermal bulk modulus of gas is equal to the pressure of the gas at that instant of time or B=p ∴p=ΔV/VΔp ⇒Δp=−VpΔV ⇒AF=−VpAx ⇒F=−VpA2x
This equation is similar to F=−kx
where k= force constant of spring,
So, k=VpA2
Hence, angular frequency ω=mk=mvpA2 mV(mg)A(∵p=Amg) ω=VAg