#### Problem 67E

67. Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure $P$ of the gas is inversely proportional to the volume $V$ of the gas.

(a) Suppose that the pressure of a sample of air that occupies $0.106 \mathrm{~m}^{3}$ at $25^{\circ} \mathrm{C}$ is $50 \mathrm{kPa}$. Write $V$ as a function of $P$.

(b) Calculate $d V / d P$ when $P=50 \mathrm{kPa}$. What is the meaning of the derivative? What are its units?