From a human health perspective, small particulate matter $($PM$)$ can be harmful when inhaled. A

large source for particles in your home is food cooking and you will similarly see large emissions coming

from an outdoor BBQ$.$ You decide to host a big BBQ party with some cooking indoors and some

outdoors. Your home is $250m^3$ and the air inside it is well mixed with an air exchange rate of $0\mathrm{.}5h{r}^{-1}.$

Your stovetop preparations are emitting a steady $800\frac{g}{h}r$ and your friends grilling outside are

producing a constant $10\frac{g}{m^3}$ for PM that is entering the home. You know you want to keep the air

clean, so you also have a filter running inside that gives a first$-$order decay constant for PM of $0\mathrm{.}48h{r}^{-1}.$

Assume that all of the following questions are coming after the system has reached steady state.

The parts to this question walk you through the steps of setting up and solving a mass balance problem as

demonstrated in class. Please apply this format $($include all the steps shown in a$-$d$)$ to all subsequent

problems involving mass balances for full credit. These steps will also be required on the exams.

a$)$ Draw a box model corresponding to the problem statement above, labeling all mass fluxes into, out of$,$

and within the system boundaries.

b$)$ Write the general mass balance equation for PM in the system you illustrated in $($a$),$ then explain which

$($if any$)$ terms can be cancelled.

c$)$ Rearrange your equation from $($b$)$ to solve for the steady$-$state concentration of PM inside your home

in terms of variables $--$ no numbers yetII

d$)$ Now use the values given in the problem statement to solve for the steady$-$state concentration of PM

inside your home $($in $\frac{g}{m^3}).$ Assume all of the PM from the smoke can be classified as PM ${?}_{25},$ which has a

National Ambient Air Quality Standard $($NAAQS$)$ of $12u\frac{g}{m^3}.$ Is the air you're breathing safe?

e$)$ Now turn off the filter that is removing the particles at $0\mathrm{.}48h{r}^{-1}$ first order decay. Calculate the new

steady$-$state concentration inside your home $($in $\frac{g}{m^3}).$ Are you safe? b$)$ Write the general mass balance equation for PM in the system you illustrated in $($a$),$ then explain

which $($if any$)$ terms can be cancelled.

$d\frac{M}{d}t=$ INPUTS$-$OUTPUTS$-$filtration

Steady $d\frac{M}{d}t=0$

$0=$ Q$\_$cook $+$ C$\_$outV$-$C$\_$inV

I want to know if i am right for part b and need help with part E