# Homework Help: What Computer Program to Use?

1. Aug 12, 2015

### Crush1986

1. The problem statement, all variables and given/known data
So, I want to make a table and a graph of the multiplicities of a system with two Einstein Solids. I was trying to use Excel but the numbers I guess were too big (300!) being the biggest. There are many more problems I'd like to do where there will be larger numbers too. Can anyone suggest a good program that I could use to achieve these goals? Thank you I appreciate it!!

2. Relevant equations
(q+N-1)!/q!*(N-n)!

3. The attempt at a solution
Tried in excel and got error #NUM!

2. Aug 12, 2015

### SteamKing

Staff Emeritus

If you want to calculate with the factorials of large numbers, like 300!, Excel is not the tool to use. You'll either have to do some separate off-sheet simplifications or use a symbolic math package, like Maple, MathCAD, or Mathematica. These symbolic math packages can work through the arithmetic and even evaluate 300! if that's what you desire.

3. Aug 12, 2015

### BvU

Generally, when working with such numbers, you don't really need all the digits of the value and you can make do with a (very good) approximation using Stirlings's formula:
$$ln(n!) = n\ln n - n$$and if n is big enough, you can even omit the last term (odd as it may seem).

4. Aug 12, 2015

### Crush1986

Aye, it's a good idea. The problems I wanted to do though want it done with a computer and with the multiplicities without taking the natural log unfortunately :(. I'm just not that great with any other program at setting up calculations, tables, and making graphs. If only Excel could just handle very large numbers.. ugh.

5. Aug 12, 2015

### BvU

I see. On the other hand, in considerations on Einstein solids such as here , they jump to Stirling pretty quickly too !

6. Aug 12, 2015

### Crush1986

Oh yeah. Looks precisely like the book I'm using to self-study at the moment. I'm starting the class 9/28 I believe. Just getting a head start because I heard that it's a pretty hard class. The book is "Thermal Physics" By Shroeder. So far I like it, it's easy to read, and I can follow pretty much all of the derivations. The book lacks hugely though in examples and problems. I've been trying to find another introductory book that covers the same content and has examples. Haven't really found a suitable one though. I have a few other thermo books but most are a tad more advanced. Also they don't have many problems either.

7. Aug 12, 2015

### BvU

Well, at least I can guess where the 300 comes from: figure 2.5 ? So for
$\Omega_A (q_A = 100) = {(100 + 300 - 1)!\over 100 ! (300-1)! }$ we have $$\ln\Omega = 399 \ln 399 - 399 - (100 \ln 100 - 100 + 299 \ln 299 - 299) = 224.65 \ \Rightarrow \Omega = 3.7 \times 10^{97}$$ not so good -- seemingly (*).

If we fall back to the more accurate version ($ln(n!) = n\ln n - n + {1\over 2} \ln(n\pi)$), that becomes $1.68 \times 10^{96}$, so spot on. Same for the other numbers.

(*) Don't let this lure you into thinking Stirling is useless: in statistical physics you deal with the order of NA particles, not with a few hundred. But even here, the figure looks exactly the same: half-width is the same, etc. And the entropy is $k\ln\Omega$ so that's practically right also !

8. Aug 12, 2015

### Crush1986

Thx! Yah I was about to give it a try using the approximations of the numbers soon. To see how closely the graph looked to 2.5. I had read that it wouldn't be as sharp. But at least it would show me visually which multiplicies were the most probable.