Bulk Modulus of an Ideal Gas the equation of state (the equation relating pressure, volume, and temperature) for an ideal gas is pV = nRT, where n and R are constants.
(a) Show that if the gas is compressed while the temperature T is held constant, the bulk modulus is equal to the pressure.
(b) When an ideal gas is compressed without the transfer of any heat into or out of it, the pressure and volume are related by pV' = constant, where 'Y is a constant having different values for different gases. Show that, in this case, the bulk modulus is given by B = 'Yp