Questions

1. How many pound moles of gas are in the system we have chosen for the Los Angeles basin if the temperature is 75°F and the pressure is 1 atm?

2. What is the rate, $F_{CO,A}$, at which all autos emit carbon monoxide into the basin ($\frac{lb*(moles\ of\ CO)}{h}$)?

3. What is the volumetric flow rate ($\frac{ft^3}{h}$) of a 15 mph wind through the corridor 20 miles wide and 2000 feet high?

4. At what rate, $F_{CO,S}$, does the Santa Ana wind bring carbon monoxide into the basin ($\frac{lb*(moles\ of\ CO)}{h}$)?

5. Assuming that the volumetric flow rates entering and leaving the basin are identical $\nu = \nu_0$ show that the unsteady mole balance on CO within the basin becomes $F_{CO,A} + F_{CO,S} - v_OC_{CO} = V(\frac{dC_{CO}}{dt})$

6. Verify that the solution to the previous equation is $t = \frac{V}{\nu_0}ln(\frac{[F_{CO,A}+F_{CO,S}]-\nu_0C_{CO,O}}{[F_{CO,A}+F_{CO,S}]-\nu_0C_{CO,f}})$

7. If the initial concentration of carbon monoxide in the Los Angeles basin before the Santa Ana wind starts to blow is 8 ppm $(2.04 * 10^{-8} \frac{lb\ mol}{ft^3})$, calculate the time required for the carbon monoxide to reach a level of 2 ppm.

8. There is heavier traffic in the L.A. basin in the mornings and in the evenings as workers go to and from work in downtown L.A. Consequently, the flow of CO into the L.A. basin might be better represented by the sine function over a 24-hour period. $F_{CO,A} = a + b*sin(\frac{\pi t}{6})$ The time, t = 0, starts at midnight and $a = 35,000 \frac{lb\ mol}{h}$ and $b = 30,000 \frac{lb\ mol}{h}$. The general material balance equation now becomes $a + b*sin(\frac{\pi t}{6}) + F_{CO,S} - v_OC_{CO} = V(\frac{dC_{CO}}{dt}).$

Using Polymath

1. Smog begins to build up again immediately after a Santa Ana wind passes through the basin. The volumetric flow rate through the basin has dropped to $1.67 * 10^{12} \frac{ft^3}{hr}$ (1.5 mph). Plot the concentration of carbon monoxide in the basin as a function of time for up to 72 hours and just after a Santa Ana wind. The initial concentration of CO is 0.08 ppm $(2 * 10^{-10} \frac{lb mol}{ft^3})$.

2. Plot the concentration of carbon monoxide as a function of time $t$ up to 48 hours for the case when a Santa Ana wind begins to blow after the 48 hours buildup of CO.

3. Vary the parameters, $\nu_0 , a, b$, and write a paragraph describing what you find.