Chapter 5, Problem 5.84P

Interpretation Introduction

(a)

Interpretation:

The given equivalent expression for SRK equation of states is to be derived.

Concept introduction:

SRK equation of states is defined as:

$P=\frac{RT}{\hat{V}-b}-\frac{\alpha a}{\hat{V}\left(\hat{V}+b\right)}$ ....... (1)

Here, $P$ is the pressure of the system, $T$ is the temperature of the system, $\hat{V}$ is the specific volume of the gas, $R$ is the universal gas constant, $a,b,\text{ and }\alpha$ are the parameters dependent on critical temperature $\left(T_C\text{ K}\right)$, critical pressure $\left(P_C\right)$, and acentric factor $\left(\omega \right)$ of the gas.

Interpretation Introduction

(b)

Interpretation:

A spreadsheet is to be prepared to calculate the specific volume $\left(\hat{V}\text{ L/mol}\right)$ of the given gas.

Concept introduction:

SRK equation of states is defined as:

$P=\frac{RT}{\hat{V}-b}-\frac{\alpha a}{\hat{V}\left(\hat{V}+b\right)}$ ....... (1)

Here, $P$ is the pressure of the system, $T$ is the temperature of the system, $\hat{V}$ is the specific volume of the gas, $R$ is the universal gas constant, $a,b,\text{ and }\alpha$ are the parameters dependent on critical temperature $\left(T_C\text{ K}\right)$, critical pressure $\left(P_C\right)$, and acentric factor $\left(\omega \right)$ of the gas.

The expression to calculate $\text{'}a\text{'}$ is:

$a=0.42747\frac{{\left(R{T}_C\right)}^2}{P_C}$ ....... (2)

The expression to calculate $\text{'}b\text{'}$ is:

$b=0.8664\frac{R{T}_C}{P_C}$ ....... (3)

The expression to calculate $\text{'}\alpha \text{'}$ is:

$\alpha ={\left[1+m\left(1-\sqrt{T/T_C}\right)\right]}^2$ ....... (4)

Here, $m$ is given by:

$m=0.48508+1.55171\omega -0.1561{\omega }^2$ ....... (5)

The ideal equation of states for an ideal gas is:

$P\hat{V}=RT$ ....... (6)

Here, $P$ is the pressure of the system, $T$ is the temperature of the system, $\hat{V}$ is the specific volume of the gas, and $R$ is the universal gas constant.

The goal seek tool of excel is an iterative method to calculate the value of a variable using another variable of which the first variable is a function and setting the goal for the first variable.

Interpretation Introduction

(c)

Interpretation:

The value of specific volume for the given gas is to be calculated using root finding method.

Concept introduction:

SRK equation of states is defined as:

$P=\frac{RT}{\hat{V}-b}-\frac{\alpha a}{\hat{V}\left(\hat{V}+b\right)}$ ....... (1)

Here, $P$ is the pressure of the system, $T$ is the temperature of the system, $\hat{V}$ is the specific volume of the gas, $R$ is the universal gas constant, $a,b,\text{ and }\alpha$ are the parameters dependent on critical temperature $\left(T_C\text{ K}\right)$, critical pressure $\left(P_C\right)$, and acentric factor $\left(\omega \right)$ of the gas.

The expression to calculate $\text{'}a\text{'}$ is:

$a=0.42747\frac{{\left(R{T}_C\right)}^2}{P_C}$ ....... (2)

The expression to calculate $\text{'}b\text{'}$ is:

$b=0.8664\frac{R{T}_C}{P_C}$ ....... (3)

The expression to calculate $\text{'}\alpha \text{'}$ is:

$\alpha ={\left[1+m\left(1-\sqrt{T/T_C}\right)\right]}^2$ ....... (4)

Here, $m$ is given by:

$m=0.48508+1.55171\omega -0.1561{\omega }^2$ ....... (5)