Question
In: Physics
A solid surface is in diffusive and thermal equilibrium with a monatomic ideal gas at temperature...
A solid surface is in diffusive and thermal equilibrium with a monatomic ideal gas at temperature t and chemical potential μ. An adsorption site on the solid surface can be either empty (energy ε0 = 0), singly occupied (ε1 = ε), or doubly occupied (ε2 = 2ε) by an atom from the gas. If two atoms adsorb onto the same site, they also interact by a vibrational mode of frequency w. Thus, the energy of a doubly occupied site can take on the values ε2 + n!w, where n = 0, 1, 2,….
a) What are the limiting probability ratios when the vibrational frequency is large
such that ℏ? ≫ ??
b) Prove that when the vibrational frequency is very small (ℏ? ≪ ?), double
occupancy becomes strongly favored.
Solutions
genius_generous answered 2 years agoRelated Solutions
A solid surface is in diffusive and thermal equilibrium with a monatomic ideal gas at temperature...
A solid surface is in diffusive and thermal equilibrium with a
monatomic ideal gas at temperature t and chemical potential μ. An
adsorption site on the solid surface can be either empty (energy ε0
= 0), singly occupied (ε1 = ε), or doubly occupied (ε2 = 2ε) by an
atom from the gas. If two atoms adsorb onto the same site, they
also interact by a vibrational mode of frequency w. Thus, the
energy of a doubly occupied site can...
If 6.00 moles of a monatomic ideal gas at a temperature of 260 K are expanded...
If 6.00 moles of a monatomic ideal gas at a temperature of 260 K
are expanded isothermally from a volume of 1.07 L to a volume of
4.61 L .
Calculate the work done by the gas.
Calculate the heat flow into or out of the gas.
If the number of moles is doubled, by what factors do your
answers to parts A and B change?
two moles of a monatomic ideal gas are compressed in a cylinder at a constant temperature...
two moles of a monatomic ideal gas are compressed in a cylinder
at a constant temperature of 85 c until the original pressure has
tripled?
a)what is the work done on the gas?
b)How much heat is transfered out of the gas?
A monatomic ideal gas in a cylinder is held at a constant
temperature 230kpa and is cooled and compressed from 1.7 to 1.2
a) what is the internal energy of the gas?
b)How much heat is transferred out...
A monatomic ideal gas has an initial temperature of 381 K. This gas expands and does...
A monatomic ideal gas has an initial temperature of 381 K. This
gas expands and does the same amount of work whether the expansion
is adiabatic or isothermal. When the expansion is adiabatic, the
final temperature of the gas is 290 K. What is the ratio of the
final to the initial volume when the expansion is isothermal?
We start with 5.00 moles of an ideal monatomic gas with an initial temperature of 133...
We start with 5.00 moles of an ideal monatomic gas with an
initial temperature of 133 ∘C. The gas expands and, in the process,
absorbs an amount of heat equal to 1300 J and does an amount of
work equal to 2200 J Use R = 8.3145 J/(mol⋅K) for the ideal gas
constant.
The temperature of 2.00 mol of an ideal monatomic gas is raised 15.0 K at constant...
The temperature of 2.00 mol of an ideal monatomic gas is raised
15.0 K at constant volume. What are (a) the work W done by the gas,
(b) the energy transferred as heat Q , (c) the change
?Eint in the internal energy of the gas, and (d) the
change ?K in the average kinetic energy per atom
For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2100 K,...
For the thermal radiation from an ideal blackbody radiator with
a surface temperature of 2100 K, let Ic represent the intensity per
unit wavelength according to the classical expression for the
spectral radiancy and Ip represent the corresponding intensity per
unit wavelength according to the Planck expression. What is the
ratio Ic/Ip for a wavelength of (a) 400 nm (at the blue end of the
visible spectrum) and (b) 210 μm (in the far infrared)? (c) Does
the classical expression...
A monatomic ideal gas of N atoms has initial temperature T0 and a volume V0, the...
A monatomic ideal gas of N atoms has initial temperature
T0 and a volume V0, the gas is allowed to
expand slowly to fill a final volume of 7V0 in the
following ways:
At constant temperature
At constant pressure
Adiabatically
For each case (a you must determine i, ii, and iii, for b and c
do the same) determine (i) the work done by the
gas, (ii) the amount of energy transferred to the
gas by heating, and (iii) the...
An ideal monatomic gas at an initial temperature of 500 K is expanded from 5.0 atm...
An ideal monatomic gas at an initial temperature of 500 K is
expanded from 5.0 atm to a final pressure of 1.0 atm. Calculate
w, q, DU, and (where applicable)
DH and DT when the expansion is performed (a)
reversibly and isothermally, and (b) reversibly and
adiabatically.
Help Please!!!
1. Consider a gas of molecules in thermal equilibrium with temperature T and a number n...
1. Consider a gas of molecules in thermal equilibrium with
temperature T and a number n per area, confined to a 2-D flat
surface.
-What is the kinetic energy per area of the gas?
-What is the force per length that these molecules exert on an
edge of the surface?
-If there are diatomic molecules, what is the rotational energy
per area of the gas? (Assume that each atom of each molecules is
confined to a flat surface)
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