ENGR263 2018 Q A1 (ENGR5002)

ENGR263 2018 Q A1Past paperOld spec ENGR2632:125 marks30 min

ENGR263 Processes of Heat and Mass Transfers 2018 Section A Q A1[VALID] official answers

Answer ALL parts (a) - (g).

An open cylindrical tank of 6 m diameter contains benzene at $22^\circ\mathrm{C}$ . The tank is exposed to the atmosphere in such a manner that the liquid is covered with a stagnant film of vapour estimated to be 5 mm thick. The concentration of benzene in the bulk of the vapour phase is assumed to be negligible. The saturated vapour pressure of benzene at $22^\circ\mathrm{C}$ is 100 mmHg.

Data: $1\ \mathrm{atm} = 1.013 \times 10^5\ \mathrm{Pa} = 760\ \mathrm{mmHg}$ , $R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$ . The effect of pressure and temperature changes from ( $P_1$ , $T_1$ ) to ( $P_2$ , $T_2$ ) on gaseous diffusivity is $D_{AB,T_2,P_2} = D_{AB,T_1,P_1}\left(\dfrac{P_1}{P_2}\right)\left(\dfrac{T_2}{T_1}\right)^{3/2}$ (T in K).

Formulas you may need

Diffusion through a stagnant gas: $N_A = \dfrac{PD_{AB}}{RT\delta}\ln\dfrac{P - p_{A2}}{P - p_{A1}} = \dfrac{PD_{AB}}{RT\delta}\,\dfrac{p_{A1} - p_{A2}}{p_{B,lm}}$ (on the formula sheet)
Pressure and temperature correction $D_{AB,T_2,P_2} = D_{AB,T_1,P_1}\dfrac{P_1}{P_2}\left(\dfrac{T_2}{T_1}\right)^{3/2}$ (on the formula sheet; also given in the question)
Rate = flux x area; mass rate = molar rate x $M$ (learn this)

(a)
Calculate the flux of mass transfer of benzene $N_{benzene}$ in $\mathrm{mol/(m^2\,s)}$ if the diffusivity of benzene in air at $22^\circ\mathrm{C}$ is $0.094\ \mathrm{cm^2/s}$ (no need to derive the model of the flux).
N_A =mol m^-2 s^-1
[10]2:2
(b)
Calculate the rate of diffusion of benzene in mol/day.
rate =mol/day
[3]
(c)
Calculate the rate of diffusion of benzene in kg/day, if the molecular weight of benzene is 0.078 kg/mol.
rate =kg/day
[2]
(d)
What is the value of the loss of benzene from this tank in pounds sterling per day, if benzene is worth 0.25 GBP/kg?
loss =GBP/day
[3]
(e)
If a floating roof is used to decrease the losses, what is the diameter of the roof needed to reduce the loss in rate of benzene by 95 %?
d_roof =m
[2]
(f)
An increase of the total pressure would have a positive effect on the loss. What is the total pressure required to save 50% of the loss in benzene rate?
P_2 =mmHg
[3]
(g)
A decrease of temperature would have a positive effect on the losses. What is the saving in losses in percent (%) of benzene rate, if temperature drops by 5 %? Assuming the saturated vapour pressure of benzene remains constant.
saving =%
[2]