Arowerall questions inthe Engineering Homevork Format $(8$ pts$).$

wirite in pencil, neathy! If it's the only vay youcan be neat, use block lettering. Showryour work. Llse proper Significant Figures. State vour assumptions.

$1.(6$ pts$)$ Canvert the ail flaw rate fram an ail spill fram

$43878$ barrels afail per daytacubic meters per haur.

A barrel af ail is $42$ gallans $($nat exact$).$

$2.(8$ pts$)$ An electric water heater runs far $2\mathrm{.}0$ haurs ta raise water temperature.

Determine the amaunt af elect ric energy used by the heater in kWh AND kJ$.$

$2\mathrm{.}5$ kW is the assumed pawer cansumptian af the elect ric water heater.

$3.(4$ pts$)$ Pravide the MLT$-$based fundamental dimensians fartarque $[$ N m$].$

$($E$.$g$.,$ the MLT$-$based fundamental dimensians farvelacity is L$/$T $($length$/$timeh$/.4.(6$ ptsi Let's sayy you have an equation q $\backslash (=\backslash$mathrm$\{$kA$\}\backslash )($T$/$ L $?.$

This is from a courseyou might takecalled Heat Transfer Pracesses.

The equation solues for the tatal heat transfer rate

$\backslash (4[$W$]\backslash )$ by canductian acrossa salid of length $\backslash ($ L $\backslash )$

The cross$-$section of the salid is represented by the area A and

the temperature difference between the twa sides is represented by $\backslash ($ T $\backslash ).$

k is a material property of thesolid. What arethe dimensions of kin metric units?

$5.(6$ pts$),$ The walumet ric flew rate af a liquid is given by the walume of flow per unit time, while the mass flow rate af a liquid is given by the quant ity of mass flawing per unit time. What fluid property is multiplied byvalumetric flow rate to determine mass flow rate? Hint: divide Mass flow rate units by Valumet ric flow rate units.

$6.(8$ pts$)$ A bacterial grawt h ratewas tound to fallow an expenential relatianship with time. When the rater $($in cells$/$h$)$ was platted as a functian of time $\backslash ($ t $\backslash )($in h$),$ whereh $=$ haurs, the relatianship was determined ta be:

$\backslash [$

r$=10\mathrm{.}0\backslash$mathrm$\{$e$\}^\{0\mathrm{.}05$ t$\}$

$\backslash ]$

What aret he units of thesonstants $(10\mathrm{.}0$ and $0\mathrm{.}05)$ in the equatian?

Hint: thee raised ta $\backslash (0\mathrm{.}5$ t $\backslash )$ must be unit less.

Write the linearized farm of the equation and

determine which axes ta use ta make this type af relatianship plat linearly. $7.[6$ pts An experimental relatianship between Current $($I$\backslash \}3,$ Time $\backslash (\backslash \{$t$\backslash \}\backslash )$ is shown in Figure $1.$

Determine the slapeand the intercept af the line fincluding units$)$ by interpreting thechart.

rig wre $1.$ Current vs time resut ts yrom on experwment Hint: Read value of intercept aff af Chart and use line $($net data prints$)$ tre determineslape. Get the units from the chart axes. $8.(9$ pts$)$ The Freundlich isat herm equatian can be used ta predict the adsorptign af gas malecules an a salid surface, here: $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )$ an Activated Chariaal.

$\backslash [$

q$=$k P$^\{1/$ n$\}$

$\backslash ]$

where $\backslash ($ q$=\backslash )$ mal gas a dsorbed per g salid and $\backslash ($ P$=\backslash )$ pressure $($Pa$).$

The canstants $\backslash ($ k $\backslash )$ and $\backslash ($ n $\backslash )$ arefar a given adsorbate and adsarbent at a given temperature. Experimental resultsareshawn in Figure $2.$ In the Trendline eauation. vis a and x is P$.$

The expanent $\backslash (1/$ n $\backslash )$ must be unit less, thus $\backslash ($ n $\backslash )$ is unit less.

$($a$)$ Repart kand n praperly $($Use Trendline equation$)$

Nate: the units of $"$pl$/"$are the units af P raised ta the $\backslash (1/$ n$^\{\backslash$text $\{$th $\}\}\backslash )$ power.

$($b$)$ What is the linearized form of the Freundlich isatherm? Use lagarithms.