Chapter 1, Problem 1.14P

Interpretation Introduction

Interpretation:

The values of a and b in the van der Waal equation of argon has to determined using the given parameters.

Concept introduction:

Ideal gas equation,

$\text{PV}\text{=}\text{nRT}\boxed{\begin{array}{l}\text{Where,}\\ \text{P}\text{:}\text{Pressure}\\ \text{V:}\text{Volume}\\ \text{n:}\text{Number}\text{of}\text{moles}\\ \text{R:}\text{Gas}\text{constant}\\ \text{T}\text{:}\text{Temperature}\end{array}}$

Virial equation: This is an equation of state for real gases in Z as a power series in terms of $\frac{1}{V_m}$ for a pure gas.

$Z=\frac{P{V}_m}{RT}=1+\frac{B}{V_m}+\frac{C}{V_m^2}+\mathrm{.....}$

B and C are the second and third virial coefficients and both are temperature dependent.

Van der Waals equation:

The deviation from ideal gas law was accounted using two constants, a and b and was given by an equation called van der Waals equation which is similar to ideal gas law as follows,

   $\left(\text{P+}\frac{{\text{n}}^{\text{2}}\text{a}}{{\text{V}}^{\text{2}}}\right)\left(\text{v-nb}\right)\text{=}\text{nRT}$

  Where,

a and b are constants

P is the pressure

V is the volume

T is the temperature

R is molar gas constant

n is the mole

Using van der Waal’s equation, the pressure can be determined as,

$P=\text{}\frac{nRT}{V-nb}-a{\left(\frac{n}{V}\right)}^2$