ENGR-1100 Introduction to Engineering Analysis

1
Lecture 11a Ideal gas

• Number of states and density of states
• Partition functions q and Q
• Thermodynamic Functions
• Problem 12.9

2
Single molecule translational energy states
From quantum mechanics states of translational
energy are enumerated by three integer numbers,
l, m, n.
Number of states within radius R,
Number of states within energy ?
3
Density of states
Number of states with energy from 0 to
? Number of states with energy from ? to ?
d? - g(?)d?, where g(?) density of states
4
Partition function for translations qt - single
particle
By definition For a gas not close to T 0,
there is a huge number of states within a given
energy range, thus the sum can be replaced with
integral With substitution the integration
gives
5
Partition function Q - many particles
For indistinguishable particles
6
Thermodynamic functions
show
show
7
Thermodynamic functions II
8
Problem 12.9
Determine the entropy change when two gases with
number of moles N1 and N2, are initially in
volumes V1 and V2 , such that V2/ V1 N2/ N1,
are allowed to mix in the combined volume V1
V2.