Page 500 - Advanced thermodynamics for engineers

492 CHAPTER 20 IRREVERSIBLE THERMODYNAMICS

where
~
N ¼ Avogadro’s number.
The groups of terms can be defined in the following way:

p h density
~
NkT
1=2

kT
h velocity
2m
3
kT h energy:
2
~ 1=2
~
Nm and 4N are weighting factors:
p 1=2 3p 1=2
Thus

_ n c
¼ density mean velocity:
A
E _
¼ density mean velocity mean energy
A
The weighting factors show that the particles passing through area A carry with them an unrep-
resentative sample of the energy of the system from which they come.
This example can be expanded into an apparatus which contains two systems separated by a porous
wall. It will be assumed that the pores in the wall are much shorter than the mean free path of the
molecules. The system is shown in Fig. 20.8. The gases on either side of the partition are the same, but
one side of the system is heated and the other side is cooled.
From Eqn (20.114) the net flux of molecules passing through the wall is given by

0 0
_ n _ n c 1=2 p p
c
¼ð2pkmÞ p ffiffiffiffiffi p ffiffiffiffi (20.118)
A T 0 T

p p'
.
Cooling Heating
.
- Q T T' + Q

Porous
wall
FIGURE 20.8
Arrangement for flow through a porous plug.