Q. A piston of cross-section area is fitted in cylinder in which gas of volume at pressure is enclosed. Gas obeys Boyle's law, what is angular frequency it piston is displaced slightly?

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Solution:

Since, gas obey’s Boyle’s law, so it is isothermal process.
The bulk modulus for gas is given by

But as gas obeys Boyle’s law,so
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





This equation is similar to

where force constant of spring,
So,
Hence, angular frequency