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ENGR5003 / Week 3
Lecture 7 example - nitrogen vessel by ideal gas, van der Waals and Redlich-KwongTutorialCurrent spec2:215 min

ENGR5003 Lecture 7 example (slides 16-18)

Nitrogen is filled in a vessel with a volume of 0.425 m30.425\ \mathrm{m^3}. The pressure and temperature of the nitrogen are 16.21 MPa and 189 K respectively. Determine the mass of the nitrogen by (a) the ideal gas model, (b) the van der Waals equation and (c) the Redlich-Kwong (R-K) equation.

Data: M=28.01 kg/kmolM = 28.01\ \mathrm{kg/kmol}, R=8314.5 J/(kmol K)R = 8314.5\ \mathrm{J/(kmol\,K)}. Van der Waals constants for nitrogen: a=1.361×105 Pa m6/kmol2a = 1.361 \times 10^5\ \mathrm{Pa\,m^6/kmol^2} (=0.1361 Pa m6/mol2= 0.1361\ \mathrm{Pa\,m^6/mol^2}), b=0.0385 m3/kmolb = 0.0385\ \mathrm{m^3/kmol}. For R-K use the critical point Tc=126.2 KT_c = 126.2\ \mathrm{K}, pc=3.39 MPap_c = 3.39\ \mathrm{MPa}.

Formulas you may need
  • Ideal gas: pV=nRTpV = nRT, m=nMm = nM (on the formula sheet)
  • Van der Waals: p=RTVm−b−aVm2p = \dfrac{RT}{V_m - b} - \dfrac{a}{V_m^2} (learn this; Lecture 7, marked "for students who are interested")
  • Redlich-Kwong: p=RTVm−b−aT0.5Vm(Vm+b)p = \dfrac{RT}{V_m - b} - \dfrac{a}{T^{0.5}V_m(V_m + b)}, a=0.42748R2Tc2.5pca = \dfrac{0.42748R^2T_c^{2.5}}{p_c}, b=0.08664RTcpcb = \dfrac{0.08664RT_c}{p_c} (learn this; Lecture 7)
  • Compressibility factor: Z=pvRgTZ = \dfrac{pv}{R_gT} (learn this)
  1. (a)
    Ideal gas model.
  2. (b)
    Van der Waals equation (p+aVm2)(Vm−b)=RT\left(p + \dfrac{a}{V_m^2}\right)(V_m - b) = RT.
  3. (c)
    Redlich-Kwong equation p=RTVm−b−aT0.5Vm(Vm+b)p = \dfrac{RT}{V_m - b} - \dfrac{a}{T^{0.5}V_m(V_m + b)} with a=0.42748R2Tc2.5pca = \dfrac{0.42748R^2T_c^{2.5}}{p_c} and b=0.08664RTcpcb = \dfrac{0.08664RT_c}{p_c}.