Homework G
PHY3513
Due: April 23, 2012
1. (28.1)
2. Consider the isotherm at T as shown in the figure. At the point A, the substance is a
mixture of liquid and vapor. Suppose that the masses of liquid and vapor are ml and mv,
respectively, and m = ml + mv. The volume occupied by the mixture at A is mlvl + mvvv
where vl and vv are the specific volumes of the liquid and vapor. Show that
ml (v − vl ) = mv (vν − v) .
This relation is known as the lever rule. The ratio mv / ml is gives you the quality of the
mixture.
p
liquid
A
vapor
V
3. Show using the Clausius-Clapeyron equation for melting that the ice point of water
(273.15 K) at atmospheric pressure is 0.01 K below the triple point (273.16 K) which
occurs at a pressure of 4.58 Torr. The density of pure water is 1000 kg m-3 and the
density of ice is 916 kg m-3. The latent heat of melting is 3.34 × 105 J kg-1.
4. The equations of the sublimation and vaporization curves of a particular substance are
given by:
ln p = 0.04 – 6/T (sublimation)
ln p = 0.03 – 4/T (vaporization)
where p is in atmospheres.
(a) Find the temperature and pressure of the triple point.
(b) Show that the molar latent heats of vaporization and sublimation are 4R and 6R. You
may assume that the specific volume of in the vapor phase is much larger than those of
liquid and solid phases.
(c) Find the latent heat of fusion near the triple point. Consider a loop round the triple
point in P-T phase diagram. lSV/Ttp – lSL/Ttp – lLV/Ttp = 0
5. A glass bulb of volume Vo is evacuated. A small amount of pure liquid is introduced
in the volume and the glass bulb is sealed. The liquid-vapor interface is observed in the
glass bulb as shown in the figure below.
(a) Describe what you would observe as the temperature is raised following the path
shown in the figure (x Æ y Æ z). Vo is significantly larger than the critical volume (Vc) of
the liquid.
(b) If Vo = Vc, what would you observe as the temperature is raised?
p
z
y
x
Vc
V