Boyles law is .

Where  is the pressure and  is volume of gas and  is constant.

(a)

Find the rate of change of volume.

Consider .

.

Differentiate on each side with respect to .

(b)

When a gas is kept in constant temperature, then the volume depends on pressure.

From Boyles law, .

At the beginning pressure will increase rapidly, so volume will decrease more rapidly at the beginning.

(c)

Isothermal compressibility :

.

From the part (a), we have .

Substitute  in .

From the Boyles law : .

.

Substitute  in .

.

(a).

(b) At the beginning pressure will increase rapidly, so volume will decrease.

(c) Isothermal compressibility .