Problems and Solutions on Thermodynamics and Statistical Mechanics

398 Problem8 El Solutiotu on Thermodynam'c~ €4 Statistical Mechanics

Fig. 2.46.

Solution:
The temperature at z can be written as

T = To + ATCOS - +PO

(,lX )

Then the change of temperature due to thermal conduction is

6T = -21 (z)

(";" )

471.1

x

= -ATsin -+PO.

Thus

6T 471.1

• 
  
  
  
  • -sin (y + Po).
    AT- x
    This is the fraction of AT which results from thermal conduction. The
    condition for thermal conduction to be ineffective is
  
  
  
  

6T

~ << 1,

AT

that is X >> I.

2202

Give a qualitative argument based on the kinetic theory of gases to

show that the coefficient of viscosity of a classical gas is independent of the

pressure at constant temperature.

(UC, Berkeley)

Solution:

Consider the flow of gas molecules along the z-direction whose average

velocity 5 = u, has a gradient in the y-direction. The number passing