The number of states is expressed as a function of various parameters for three systems below. For each, find an "equation of state" which gives the relationship between p, V, N, and T.
(C and b are constants.)

Please see the attached Microsoft Word document regarding specifics.

List of solved problems:
Derive Strirling's approximation for N!.
Derive the Gaussian approximation of the binomial distribution.
Derive expressions for the mean and standard deviation for the binomial distribution.
Compute the pressure of an ideal Bose gas at absolute zero.
Compute the entropy of an ideal gas usi

Let [EQUATION1] with [EQUATION2] and [EQUATION3]. The idea is to write each such set in some simple canonical form.
(i) When n = 2, how many distinct knapsack sets are there? Write them out in a canonical form with integral coefficients and 1 = [EQUATION4].
(ii) Repeat for n = 3 with [EQUATION5].
*(For proper equations an

Problem attached.
(a) Find the shortest and the largest distance from the origin to the surface of the ellipsoid.
(b) Find the principal axes of the ellipsoid.

Choose one of the micro-payment systems (see e.g., http://en.wikipedia.org/wiki/Micropayment) or micro-credit system (see, e.g., http://en.wikipedia.org/wiki/Microcredit), try to describe how it works briefly. Discuss its security. 2 paragraphs is enough
With Scholarly Referencing.

As provided by E. Galua theory the general algebraic equations for a polynomial of fourth order
ax^4 + bx^3 + cx^2 + dx + f=0 (*)
is the maximum order type of algebraic equations the solution to which one can write down in radical expressions.
Among all the equations of fourth

A) Classify and find general expressions for the characteristic coordinates for the equation {see attachment}
b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that {see attachments} where F and G are arbitrary functions of their ar

Three capacitors(4.0, 6.0 and 15.0 Micro Farads) are connected in series across a 50 volts battery. Find the voltage across the 4.0 micro Farad capacitor. Answer in volts.