GREPhysics.NET
GR | # Login | Register
   
  GR8677 #15
Problem
GREPhysics.NET Official Solution    Alternate Solutions
Verbatim question for GR8677 #15
Statistical Mechanics}Probability

Probability is mostly common sense and adhering to definitions.

The probability that a gas molecule or atom is in the small cube is P(in)=1E-6. The probability that it's not in that small cube is P(not)=1-1E-6. Assuming independent gas molecules or atoms, i.e., the usual assumption of randomness in Stat Mech, one gets, P(N gas atoms)=\left(1-1E-6\right)^N.

The answer is thus C.

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
There are no Alternate Solutions for this problem. Be the first to post one!
Comments
ubaraj
2007-11-01 01:15:13
the volume is 1. There can be no He atoms in the volume 10E-6. So all N atoms have to be within the volume (1-10E-6), and so the probability becomes (1-10E-6)^N. The choice is C!!NEC
Furious
2007-08-17 15:40:58
You really just need to look at the limiting factors in this problem.

When N is 0 the probability should be 1. That eliminates A and D.

When N is extremely high, the probability should go to 0. That eliminates E, (not that any of us thought it was E)

So that leaves us with B and C. Which both match the limiting cases, but just think about it when N is 1. When N is one there should be a very high chance that it is not in the specific 1e-6 area.

For B, the probability is 1e-6, not very high at all.
For C, the probability is 0.99999, pretty close to 1.

This helped me since, I get super confused whenever I think about probability.
NEC
wishIwasaphysicist
2006-01-24 11:27:10
How did you connect P(Ngasatoms) = (1-1E-6)^N to answer C?
yosun
2006-02-01 22:02:05
hi wishIwasaphysicist, because each of the N molecules are independent, the probability would be multiplicative. Thus, if the particle for each particle is P, the probability for N particles would be P^N.
Answered Question!

Post A Comment!
Username:
Password:
Click here to register.
This comment is best classified as a: (mouseover)
 
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\int_0^\infty$
$\partial$
$\Rightarrow$
$\ddot{x},\dot{x}$
$\sqrt{z}$
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
$\vec{E}$
$\frac{a}{b}$
 
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...


ShoutMix chat widget

1GHz Smartphone for 1 cent - best deal on a Samsung Galaxy Phone

Unlimited Access 24/7

Find Scholarships Today!

Search FastWeb see Green!

SL Button 125

Free 3D Virtual World. Largest User-Created Fantasy World. Don't Play, Experience. Join Now!

Bored, got time to kill, and want to earn micro-cash by mindlessly clicking on links? Join CrownGPT. Click Offers. Click the Paid to Click button... then click to your heart's delight.

90% Off + FREE SHIPPING!

FREE 3D Virtual World Chat - Join Second Life Today!