Boyle's Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant: PV = C. (a) Find the rate of change of volume with respect to pressure. dV dP = (b) A sample of gas is in a container at low pressure and is steadily compressed at constant temperature for 13 minutes. Is the volume decreasing more rapidly at the beginning or the end of the 13 minutes? Explain. From the formula for dV dP , we see that as P increases, the absolute value of dV dP . Thus, the volume is more rapidly at the beginning. (c) Write the formula for isothermal compressibility (see this example) in terms of P. β =