Document 2339791

Ben-Gurion University of the Negev
Department of Physics
Thermodynamics & Statistical Mechanics 1
‫גוריון בנגב‬-‫אוניברסיטת בן‬
‫המחלקה לפיסיקה‬
1 ‫תרמודינמיקה ומכניקה סטטיסטית‬
Exercise 10 – Chemical potential and the Gibbs energy
1. Adsorbsion of hydrogen 3D gas to a 2D surface
a. Find the chemical potential of an ideal gas in 2 dimensions
b. An H2 molecule breaks into two H atoms as it gets adsorbed on a surface, each releasing an
energy ε. (They do not stick to a specific site, but rather as a 2D gas on the surface). Find the
density of H atoms on the surface as a function of the pressure of the H2 gas
2. Law of mass action
nC v
Z 
 V 2 1C  K (T ) , where n is the density, Z
nA nB
Z1 A Z1B
is the single-particle canonical partition function, and V is the volume. K(T) is a function that depends on
temperature.
In the chemical reaction A  B  C show that
3. Water up a tree
Find the maximal height to which water can rise inside a tree under the assumption that the roots are
immersed in a water pond and the upper leaves are in air with relative humidity of ρ=0.9 (the relative
humidity is the ratio between the concentration of water in the air at a given height and the
concentration of water in the air directly above the surface of the water). Further assume that the
system is in equilibrium at a temperature of 25oC.
Guidance: calculate the chemical potential of the water vapors, under the assumption that they are an
ideal gas, at the foot of the tree and at its highest point at height h with gravity as the only external
force. Water will rise as long as the chemical potential at the top of the tree is smaller than that at the
foot of the tree.
Your answer will reveal that there must be other limitations on the height of trees (such as? how would
you modify the model?)