Question $2[30]$

$2\mathrm{.}1.$ Hydrogen can be separated from natural gas by diffusion through a round tube. The rate of separation is given by$,$

$N=2DR$

Where,

$N=$ the rate of transport of $H_2$ from the tube, gmoles$/($sec$)($cm of length of the tube$)$

$D=$ diffusion coefficient

$=$ molar density of $H_2,$ gmoles $\frac{?}{c{m}^3}$

$1$

$R=log$ mean radius of the tube, $\frac{r_2-r_1}{ln(\frac{r_2}{r_1})},$ with $r$ in $cm.$

What are the units of D$?$

$(15$ marks$)$

$2\mathrm{.}2.$ The heat capacity of a golden syrup has the units $\frac{J}{\text{g}\text{m}\text{o}\text{l}}(C)$ and is given by the following relation:

$C_P=139\mathrm{.}1+(1\mathrm{.}56{10}^{-1})T(C),$ where $Tis$ expressed $inC$

Modify the formula so that the heat capacity has the following units: $Bt\frac{u}{l{b}_{\text{m}\text{o}\text{l}}}(R).$

In the given relation, $T$ is used as a specific temperature value and not a unit temperature difference.

$T(C)=\frac{1}{1\mathrm{.}8}[T(R)-460-32]$