Chapter 10.1, Problem 21E

Carbon Dioxide Diffusion in Lungs during Breath HoldingWhen the breath is held, carbon dioxide $\left(C{O}_2\right)$ diffuses from the blood into the lungs at a steadily decreasing rate. Let $P_0$ and $P_b$ denote the pressure of $C{O}_2$ in the lungs, respectively, in the blood at the moment when the breath is held. Suppose that $P_b$ is constant during breath holding, and let $P\left(t\right)$ denote the pressure of $C{O}_2$ in the lungs at time $t>0$. Experiments show that the rate of change of $P\left(t\right)$ is proportional to the difference between two pressures $P\left(t\right)$ and $P_b$. Find an initial value problem that describes the diffusion of $C{O}_2$ in the lungs during breath holding.