Problems and Solutions on Thermodynamics and Statistical Mechanics

(^188) Problems d Soltdiotu on Thermodynamics t3 Statisticd Mechanics
Solution:
(a) Using the equation of state for an ideal gas, we get
T = pV/nk = 241 K.
(b) The population distribution is given by
Therefore
Using the given n1 and n2, we get T as follows:
99.2; 99.5; 99.0; 99.5; 100.2; 98.8 K.
The mean value is T = 99.4 K.
(c) The rate of heat intake is q = - = T-, giving
dQ dS
dt dt
T= -^9
(%)
dS
dt
We estimate - by the middle differential at t = 500s, and get
= 1.0 x 10-3J/sec.K
@ = (3.20 - 3.00)
dt 600 - 400
Therefore T = 10K.
2028
Assume that the reaction H*p+e occurs in thermal equilibrium at
T = 4000 K in a very low density gas (no degeneracy) of each species with
overall charge neutrality.
(a) Write the chemical potential of each gas in terms of its number
density [HI, [p], or [el. For simplicity you may ignore the spectrum of