ENGR266 2018 Q A1 (ENGR5003)

ENGR266 2018 Q A1Past paperOld spec ENGR2662:221 marks25 min

Answer ALL parts (a) - (d)

For this question you may need to use the attached data table for 1,1,1,2-tetrafluoroethane (HFC-134a).

Formulas you may need

Ideal gas: $PV = nRT$ , $R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$ (on the formula sheet)
Redlich-Kwong: $P = \dfrac{RT}{V - b} - \dfrac{a}{T^{1/2} V (V + b)}$ , $a = 0.42748\dfrac{R^2 T_c^{2.5}}{P_c}$ , $b = 0.08664\dfrac{R T_c}{P_c}$ (learn this)
Equivalent generic-cubic form: $a(T) = 0.42748\,\alpha(T_r)\dfrac{R^2T_c^2}{P_c}$ with $\alpha = T_r^{-1/2}$ (learn this)
R134a saturated $v_f$ , $v_g$ at the given temperature (learn this: read from the table provided)

(a)
Represent the three isothermal processes indicated by the red lines ( $T_1$ , $T_2$ and $T_3$ ) in the P-T diagram below (Figure A1) on a P-V diagram. Label the liquid and vapour regions, the critical point and the saturated liquid and saturated vapour curves.
[6]Third
(b)
Calculate the change in the specific volume of HFC-134a during vapourisation at $43^\circ\mathrm{C}$ .
dv_fg =m^3/kg
[2]
(c(i))
Calculate the pressure of 1 mole of HFC-134a in a rigid container of volume $0.001\ \mathrm{m^3}$ at $175^\circ\mathrm{C}$ according to: (i) The ideal gas equation.
P_ideal =kPa
[2]
(c(ii))
(ii) The Redlich-Kwong equation of state. The critical temperature ( $T_c$ ) for HFC-134a is $101.08^\circ\mathrm{C}$ and the critical pressure ( $P_c$ ) is 4060.3 kPa.
P_RK =kPa
[9]
(d)
What is the origin of the discrepancy between the pressures calculated using the ideal gas equation and the Redlich-Kwong equation of state?
[2]