Problem II $($old exam problem$)$

A researcher accidentally spills benzene $(C_6{H}_6,78\frac{g}{m}ol)$ on the laboratory floor. Because

benzene is a known carcinogen, the protocol is to evacuate the lab immediately. Because

there are no spill kits and protective gear available, the researcher decides to let the benzene

puddle evaporate.

The lab ventilation system creates an air flow at velocity $1\frac{m}{s}$ parallel to the surface of the

benzene puddle. You can assume that the ventilation supplies a constant flow of fresh air

$).$

The puddle can be considered rectangular with a length $L=2m,$ width $W=1m$ and depth

$d=1mm.$ You may assume that the air and benzene puddle remain at room temperature

$(25C)$ throughout the evaporation process due to the large thermal mass of the building. At

this temperature, the mass densities of benzene in the saturated vapor and liquid states are

known to be $0\mathrm{.}400$ and $900k\frac{g}{m^2},$ respectively, while the latent heat of evaporation is $400$

$k\frac{J}{k}g.$

The aim of this problem is to estimate the time for the benzene to fully evaporate. As

simplification, you may assume that during evaporation the depth of the benzene puddle

remains uniform and slowly decreases, without the area changing.

A$/$ Explain why the width $W$ of the puddle does not affect the time it takes for the puddle to

fully evaporate, but the length $L$ does.

B$/$ Use a model to estimate the diffusion coefficient of benzene in air under these conditions

and compare your result with the tabulated value of $0\mathrm{.}0962c\frac{m^2}{s}$ in the hand$-$out $($Appendix J

from the textbook$).$

C$/$ What is the initial rate $($in $\frac{g}{s})$ at which the benzene evaporates from the puddle

D$/$ How long does it take for the puddle to evaporate entirely $($in minutes$)?$

While she is waiting outside the lab, the researcher wonders how reasonable the key

assumptions are: $1)$ isothermal conditions, and $2)$ constant puddle area and only decreasing

$d$ during evaporation.

E$/$ If the isothermal assumption is not reasonable, is the actual evaporation time lower or

F$/$ If the puddle area does not remain constant, but instead slowly decreases during

evaporation as you would expect based on your experience with spills$)$ would that increase or

decrease the evaporation time? Explain your answer.