Question

Consider the Relich-Kwong equation of state P = \frac{RT}{v-b} - \frac{a}{v(v+b)\sqrt{T}}P=v−bRT​−v(v+b)T​a​

For methane, a = 32.19a=32.19 bar(m^33/(kg\cdot⋅mol))^22 K^{0.5}0.5 and b = 0.02969b=0.02969 m^33/(kg\cdot⋅mol).

Find the specific volume at the critical point predicted by this equation in m^33/kmol.​

Answer 1

Explanation:

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Answer 2

The Redlich-Kwong equation of state is given by

p=\frac{R T}{v-b}-\frac{a}{v(v+b) \sqrt{T}}p=

v−b

RT − v(v+b) Ta

where R = the universal gas constant [= 0.518 kJ/(kg K)], T = absolute temperature (K), p = absolute pressure (kPa), and v = the volume of a kg of gas (m^3/kg). The parameters a and b are calculated by

a=0.427 \frac{R^{2} T_{c}^{2.5}}{p_{c}} \qquad b=0.0866 R \frac{T_{c}}{p_{c}}a=0.427

p c R 2 T c2.5 b=0.0866R

where p_c = 4600 kPa and T_c = 191 K. As a chemical engineer, you are asked to determine the amount of methane fuel that can be held in a 3-m^3 tank at a temperature of −40 Celsius degrees with a pressure of 65,000 kPa.

Use a root-locating method of your choice to calculate v and then determine the mass of methane contained in the tank.