Problems and Solutions on Thermodynamics and Statistical Mechanics

106 Problems Ec Sddio~ on Thermodynam'cs tY Statistical Mechunics

(e) If, in the initial state, the gas in the left compartment were a mole
of argon instead of a mole of neon, which, if any, of the answers to (a), (b)
and (c) would be different?
(UC, Berkeley)
Solution:
(a) The internal energy of an ideal gas is a function dependent only on
temperature, so the internal energy of the total system does not change.
Neither does the temperature. The new equilibrium temperature is 300 K.
(b) The volume ratio is the ratio of molecular numbers, and is also the
ratio of initial pressures. Thus

VN, :VA~~ = 4: 1 = 1: n.

where n = 1/4 is the mole number of the argon gas.

(c) The increase of entropy of the system is

4 1

-R-

2 2

= R In 5 + - ln 4 = 2.0 J/K.

• 141 -

(d) The additional entropy change is

AS' = Rln(1 + n) + nRln

(e) If initially the gas on the left is a mole of argon, the answers to (a),

(b) and (c) will not change. As for (d), we now have AS' = 0.

4. CHANGE OF PHASE AND PHASE EQUILIBRIUM
   (1 106- 1147)

1106

Is the melting point of tungsten 350, 3500, 35,000, or 350,000°C?

(Columbia)

Solution:

The answer is 3500°C.