1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Change in accessible states relating to change in energy

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    A certain system has 6 × 10^24 degrees of freedom. Its internal energy
    increases by 1%. By what factor does the number of accessible states increase?

    2. Relevant equations
    [tex]\Omega = E^{N\nu/2}[/tex]
    [itex]\nu[/itex] is the degrees of freedom, and N is just 1, so we can ignore that. So the exponent is just 3x10^24
    [itex]\Omega[/itex] is the number of accessible states.
    3. The attempt at a solution

    First I replaced E with 10. And then E increased by 1% would be 10.1.
    What I was going to try to do was divide 10.1^(6x10^24) by 10^(6x10^24) to get my answer. But no calculator in the world can do that.
    So I used a calculator that can do big numbers (but not quite that big). I found that as I increased the 0's in the exponent, the exponent of my answer increased by some seemingly random number. I tried 10.1^(300)/10^(300) and then 10.1^(3000)/10^(3000), and then kept adding zeroes like that to see what kind of pattern I got.
    What I got was, as I got up to 10 zeroes, was an answer of 3x10^(129641213). If I take away a zero from the exponents in the fraction, then I just lose an exponent in the answer. So if I had 24 zeroes in my exponents in my fraction, then the answer would be roughly 3x10^(1.29x10^22).

    But this can't be the way to do this problem. Anyone have an alternative idea on how to solve this? Thanks.
     
  2. jcsd
  3. Oct 26, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try taking logarithms on both sides: the desired ratio is ##\Omega '/\Omega = \exp ...##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Change in accessible states relating to change in energy
Loading...