Document 2378300

Ben-Gurion University of the Negev
Department of Physics
Thermodynamics & Statistical Mechanics 1
‫גוריון בנגב‬-‫אוניברסיטת בן‬
‫המחלקה לפיסיקה‬
1 ‫תרמודינמיקה ומכניקה סטטיסטית‬
Tutorial 10 – Gibbs distribution & Chemical Potential (GCE)
1.
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?)
2.
Adsorbsion of hydrogen 3D gas to a 2D surface
a. Find the chemical potential of an ideal gas in 2 dimensions
b. A 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