Question

Using statistical thermodynamics prove that for one mole of a NO molecule U m=Um(0) +7/2 RT. What approximation(s) do you need to consider?

Answer #1

Thermodynamics of a single molecule:
One end of a molecule is fixed to a surface. Another end is
pressed down by the tip of an atomic force microscope, as shown
below. Using the tip of an atomic force microscope as a probe, we
measure the force of molecule retraction. The force depends on the
temperature at which the experiment is performed: f= (aT+b) x where
a and b are constants
(a) Using the thermodynamic identity for U (i.e. dU= T...

Using the utility function U(x,y)=3x+y/2, px=7, py=1,
and M=46 , what is the utility-maximizing demand for y,
y*?

Apr
Oct
12
0
2
0
4
0
36
0
2
2
7
1
67
0
30
2
4
4
1
0
7
1
4
0
2
0
16
0
15
22
268
1
12
6
73
4
40
0
2
0
30
6
11
0
16
0
10
0
317
5
13
0
1
0
26
1
4
0
58
7
4
1
13
0
30
0
6
0
33
4
5
0
2
0
1
0
4
0...

Apr
Oct
12
0
2
0
4
0
36
0
2
2
7
1
67
0
30
2
4
4
1
0
7
1
4
0
2
0
16
0
15
22
268
1
12
6
73
4
40
0
2
0
30
6
11
0
16
0
10
0
317
5
13
0
1
0
26
1
4
0
58
7
4
1
13
0
30
0
6
0
33
4
5
0
2
0
1
0
4
0...

Consider the differential equation u ′′ + bu = sin^2 (2t).
(a) For what value of b does the solution show resonance?
Clearly, explain your answer. Hint: sin2 x = 1−cos(2x) 2
(b) Consider the same differential equation but take the
non-homogeneous term to be sin4 t. For what value(s) of b does the
solution show resonance? You do not have to give an exact solution
but you do have to explain clearly your thinking using the
structure of the...

Given the following initial simplex tableau:
x y z u v w P
2 4 3 1 0 0 0 4
6 7 1 0 1 0 0 8
6 6 5 0 0 1 0 18
-8 -11 -4 0 0 0 1 0
The pivot element that would be selected if you follow the standard
convention taught in this course is the entry in row ,
column .
Now, use this pivot element and complete ONE STEP
using the simplex...

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...

=Using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 only once,
find all the possible 3 digit number plus another 3 digit number to
equal a 4 digit number. (No repetition of numbers is allowed.) One
example is 589+437=1026.
We are asked to find ALL the possibilities. I know it has to do
with combinations, but I'm not quite sure if I'm using it the
proper way.

1) You collide two cartselastically. One 2-kg cart is moving to
the right at 3 m/s, and the other is a 3-kg cart that is heading to
the left at 4 m/s. a) What are the final velocities of each cart?
b) What are the final and initial total momentums? How do they
compare? c) What are the final and initial total kinetic energies?
How do they compare?
2) You collide two carts inelastically. One 2-kg cart is moving
to...

Given that A to Z are mapped to integers 0-25 as follows.
A:0, B:1, C:2, D:3, E:4, F:5, G:6, H:7, I: 8, J: 9, K:10, L:11,
M:12, N:13, O:14, P:15, Q:16, R:17, S:18, T:19, U:20, V:21, W:22,
X:23, Y:24, Z:25.
Encrypt the following message using Vigenere Cipher with key:
CIPHER
THISQUIZISEASY
What is the ciphertext? Show your work.
PLEASE HELP

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