Chapter 5, Problem 5.81PAE

Interpretation Introduction

Interpretation:

The following figure shows the distribution of speeds for two samples of N₂ gas. One sample is at 300 K and the other is 1000 K. Which curve represents which temperature should be explained.

Concept introduction:

Theory which explains the macroscopic nature of gases and which can be utilized to explain and understand the gas laws is known as Kinetic Molecular Theory. Though, for one mole of ideal gas, it is not possible to determine the velocity for each of the molecule at every instant. Thus, the Maxwell-Boltzmann distribution is utilized to calculate the number of molecules, which are moving among the v and v + dv velocities. Presumptuous that the single-dimensional distributions are not dependent on each other, that the y and z directions velocity doesn't disturb the x velocity, for illustration, the Maxwell-Boltzmann distribution is given as follows:

$\frac{\text{dN}}{\text{N}}{\text{ = 4πv}}^2{\left(\frac{\text{m}}{\text{2πkt}}\right)}^{3/2}{\text{e}}^{\frac{-{\text{mv}}^2}{2\text{kt}}}$

Here, $\frac{\text{dN}}{\text{N}}$ is the fraction of molecules moving at velocity v to v + dv, m is the mass of the molecule,kb is the Boltzmann constantandT is the absolute temperature.