Problems and Solutions on Thermodynamics and Statistical Mechanics

386 Problems d Solutiom on Thermodynomic3 6' Statistical Mechanics

Thus the molecular flux along the pipe is

4 = -Avo An

Since

we have

1 kT

nu pa

1=-=-,

4 = Avo^1 dp

u pdz

(b) As given, p 5 lop5 rnmHg, we have

That is, the mean free path is much longer than the pipe and the above

expression for 4 is not valid. However, as the diameter of the pipe is much

smaller than its length, we have 4 = Avon.

Assume that both the initial and final states are in thermal equilibrium

at temperature T, then

dn

dt

V- =-A von ,

Hence

2194

Consider the hydrodynamical flow conditions. The cooling of the gas

during expansion can be expressed as follows, 5 = 1 + -, where To is

the temperature before expansion, T is the temperature after expansion,

M2

T 3