Question

Use
gibbs distribution to calculate the average entropy, energy and
pressure of a single classical particle of mass m, with no internal
degrees of freedom, free to move in volume V at temperature T. For
that you will need to know the volume Vd of an d-dimensional
hypersphere of the unit radius. (Vd=pi^(d/2)/gamma(d/2+1))

Answer #1

The Gibbs distribution function for the single particle is given by . So the partition function for the single particle free to move in volume V is given by

using the standard formula of Gaussian we can write this as

ones we have the partition function we can calculate the average values of E,S,P as follows

Here we calculate the partition function, molar translational
internal energy, and molar translational entropy of a monatomic
gas. The single particle translational partition function is
qtrans=VΛ3) where Λ is the thermal wavelength and teh entropy is
given by the Sackur-Tetrode equation
S=N*kB*ln((qtrans*e^5/2)/N).
A. Calculate the single particle translational partition
function q for neon gas at T=298K and V=22.4L. Assume neon behaves
ideally.
B. Based on your answer in Part A, calculate the molar
translational internal energy of neon at at...

Calculate the change in entropy for one mole of ideal gas which
expands from an initial volume of 2 L and initial temperature of
500 K to a final volume of 6 L under the following conditions.
P(initial) refers to the pressure when T(initial)= 500K,
V(initial)= 2 L.
a) Irreversible expansion against a constant pressure of
Pinitial/2
b) Irreversible expansion against a vacuum...a 'free
expansion'.
c) Adiabatic irreversible expansion against a constant pressure
of Pfinal
d) Adiabatic reversible expansion

Consider two containers,
Both have volume 0.1 m3, and pressure 106
Pa
One contains monatomic ( 3 degrees of freedom) He at T= 124 K
and
One contains diatomic (5 degrees of freedom) N2 at T
= 238 K.
A valve is opened allowing these two gases to mix. They are kept
thermally isolated from the outside.
You can treat them as ideal gases.
1)
What is the change in internal energy under this process?
2)
What is the final...

2 Equipartition The laws of statistical mechanics lead to a
surprising, simple, and useful result — the Equipartition Theorem.
In thermal equilibrium, the average energy of every degree of
freedom is the same: hEi = 1 /2 kBT. A degree of freedom is a way
in which the system can move or store energy. (In this expression
and what follows, h· · ·i means the average of the quantity in
brackets.) One consequence of this is the physicists’ form of...

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

Energy expended to drive
cyclosis in a single chloroplast cell
Use the formula (Equation 1) derived in the practical module
(included below) to calculate the energy expended to bring about
cyclosis in each of the cells of the leaves you have been
observing. Don’t forget units! Use brackets around each variable
when performing your calculations.
You must show
your working to gain full marks.
Equation 1: 6πrnV2M (Js-1
Cell-1 for a cell containing M chloroplasts)
π
3.14 (pi)
r
3.665...

1) Describe an example of each of the following that may be
found of your kitchen: Explain how your choice falls into this
category, and if there is a chemical name or symbol for it, provide
that as well. Provide a photo of your example with your ID card in
it. a) a compound b) a heterogeneous mixture c) an element (symbol)
Moving to the Caves… Lechuguilla Caves specifically. Check out this
picture of crystals of gypsum left behind in...

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