Chapter 7.7, Problem 8P

(A)

Interpretation Introduction

Interpretation:

The final pressure of supercritical methane using ideal gas law.

Concept Introduction:

Write the expression to calculate the number of moles $\left(n\right)$.

$n=\frac{M}{MW}$

Here, mass is M and molecular weight of methane is MW.

Write the expression to calculate the molar volume.

$\underset{\_}{V}=\frac{V}{n}$

Here, volume of the vessel is $V$.

Write the expression to calculate the pressure using Ideal gas.

$P=\frac{RT}{\underset{\_}{V}}$

Here, gas constant is R and temperature is T.

(B)

Interpretation Introduction

Interpretation:

The final pressure of supercritical methane using van der Waals equation.

Concept Introduction:

Write the expressions to calculate the constants of van der Waals equation of state.

$a=\frac{27R^2{T}_c^2}{64P_c}$

$b=\frac{R{T}_c}{8P_c}$

Here, critical pressure and critical temperature is $P_c$ and $T_c$ respectively.

Write the van der Waals equation of state.

$P=\frac{RT}{\underset{\_}{V}-b}-\frac{a}{\underset{\_}{V}}$

(C)

Interpretation Introduction

Interpretation:

The final pressure of supercritical methane using the Soave equation.

Concept Introduction:

Write the relationship between the parameter, m and Soave’s EOS.

$m=0.480+1.574\omega -0.176{\omega }^2$

Here, the acentric factor is $\omega$.

Write the expression to calculate the $\alpha$ expressed as a function of the reduced temperature.

$\alpha ={\left[1+m\left(1-T_r^{0.5}\right)\right]}^2$

Here, reduced temperature is $T_r$.

Write the expression to calculate the reduced temperature.

$T_r=\frac{T}{T_c}$

Here, critical temperature is $T_c$ and system temperature is T.

Write the expression to calculate the value of a at the critical point.

$a=0.42747R^2\frac{T_c^2}{P_c}\times \alpha$

Write the expression to calculate the value of b using the Soave equation.

$b=0.08664R\left(\frac{T_c}{P_c}\right)$

Write the expression for Soave equation of state.

$P=\frac{RT}{\underset{\_}{V}-b}-\frac{a}{\underset{\_}{V}\left(\underset{\_}{V}+b\right)}$

Here, system pressure is P.

(D)

Interpretation Introduction

Interpretation:

The final pressure of supercritical methane using Lee-Kesler generalized correlation.

Concept Introduction:

Write the expression to calculate the compressibility factor $\left(Z\right)$.

$Z=Z^0+\omega Z^1$

Here, compressibility of compound with $\omega =0$ is $Z^0$ and difference between $Z^0\text{and}Z$ is $Z^1$.

(E)

Interpretation Introduction

Interpretation:

The final pressure of supercritical methane using Figure 7-1.

Concept Introduction:

Write the expression to calculate the density.

$\rho =\frac{M}{V}$

Here, mass and volume of a vessel is M and V respectively.