Question

Derive the expression for the excess dimensionless entropy of mixing S E /kB as a function of polymer volume fraction, as given by the Flory model. Excess entropy is the entropy of mixing minus the ideal entropy of mixing.

Answer #1

Derive the Sacker-Tetrode Equation which is the entropy
expression for N indistinguishable ideal gas atoms of total energy
U in a container of volume V.

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...

When mixing ideal gases where S corresponds to entropy, If the
change in Stotal and Smixing are not equal to
each other, where does the difference come from? What is the
difference?

For a given utility level, U0, derive the Expenditure
function E(pr, ps, U0) for U(R,S)
= R0.8S0.2

In this problem, you will model the mixing energy of a mixture
in a relatively simple way, in order to relate the existence of a
solubility gap to molecular behavior. Consider a mixture of A and B
molecules that is ideal in every way but one: the potential energy
due to the interaction of neighboring molecules depends upon
whether the molecules are alike or different. Let n be the average
number of nearest neighbors of any given molecule (perhaps 6...

In this problem you will model the mixing energy of a mixture in
a relatively simple way, in order to relate the existence of a
solubility gap to molecular behavior. Consider a mixture of A and B
molecules that is ideal in every way but one: The potential energy
due to the interaction of neighboring molecules depends upon
whether the molecules are like or unlike. Let n be the average
number of nearest neighbors of any given molecule (perhaps 6...

Derive the log-run cost function assuming that the production
function s given by q = K+L?

Derive the long-run cost function assuming that the production
function s given by q = K+L?

The parallel plate capacitor is being charged as shown in the
Figure.
(a) Derive an expression for the induced magnetic field in both
of the regions, r < R and r > R.
(b) Find B at r = R for dE/dt = 1012 V/m-s and R = 5.0 cm.
(c) What is the displacement current in Amperes?
(d) What is the direction of the Poynting vector?
(e) Show that the rate at which energy flows into the volume
between...

In class we discussed a reversible, isothermal compression of an
ideal gas. The initial point (1) is an ideal gas in equilibrium at
pressure 1 (P1), volume 1 (V1) and temperature (T), and the final
point (2) is an ideal gas in equilibrium at pressure 2 (P2), volume
2 (V2) and temperature (T), where V2
d) For each differential step, the change in entropy is given by
dS=qrev/T =!!!"#! . Since T is constant , this express ion can be...

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