Problems and Solutions on Thermodynamics and Statistical Mechanics

396 Problems €4 Solutions on Thermodynamics €4 Statistical Mechanics

The most probable velocity is the value of v corresponding to maximum f.

From - af = 0, we get
av

up = E= 352 m/s ,

(b) The velocity distribution of the escaping molecules is given by

Fdv = Nv3e- dv ,

dF
where N is the normalizing constant. from - = 0, we get
av

Vm - - = 431 m/s

(c) The velocity of sound is

Using the adiabatic relation p = p7. const., we get

c= J7z,

where 7 = cp/c,. For argon gas, 7 = 5/3, and c = 101 m/s.

(d) The average flow velocity is

v = 1 v. $,-~"dv

• 468 m/s.

2200

Estimate, to within an order of magnitude, on the basis of-kinetic

theory the heat conductivity of a gas in terms of its temperature, den-

sity, molecular weight, and heat capacity at constant volume. Make your