All Solutions
Page 419: Practice Problems
– The total number of particles of gas in the lungs $N = 1.5 cdot 10^{23}$
– The atmospheric pressure $P = 101text{ kPa}$
– The temperature of the body $T = 310text{ K}$
To calculated the volume of the lungs we use the Ideal Gas Equation:
$$
begin{equation*}
PV = N , k , T
end{equation*}
$$
rearranging for volume
$$
begin{equation*}
V = frac{N , k , T}{P}
end{equation*}
$$
Plugging in the values we get:
$$
begin{align*}
V = frac{1.5 cdot 10^{23} cdot 1.38 cdot 10^{-23} , frac{text{J}}{text{K}} cdot 310text{ K} }{101 cdot 10^{3}text{ Pa}} = 0.00635text{ m}^3
end{align*}
$$
$$
PV=NkT
$$
So we can see that if other factor remains constant then the number of molecule $N$ is proportional to the pressure $P$. So if pressure decreases, the number of gas molecule will also decrease.