Consider a classical gas of indistinguishable particles in equilibr...

  1. Home
  2. Homework Library
  3. Physics
  4. Physics - Other
  5. Consider a classical gas of indistinguishable particles in equilibr...


Transcribed TextTranscribed Text

Consider a classical gas of indistinguishable particles in equilibrium in the grand canonical ensemble. Label the set of allowed states as {i], where state i has total energy Ei and total number of particles Ni. You can think of state i as representing some small finite cell of classical phase space. The grand canonical partition function can then be written as = = where B = 1/kBT, u is the chemical potential, and 2 = eBH is the fugacity. a) [5 pts] Write an expression that gives the probability Pi for the system to be found in a particular state i. b) [6 pts] What is the probability P(N) that the system has a given number of particles N? Express your answer in terms of L, 2 and the N-particle canonical partition function QN. c) [7 pts] Find general expressions for the average (N), and variance (N2) - (N)2, of the number of particles in terms of appropriate derivatives of In C. Now suppose that the particles are non-interacting. d) [7 pts] Show that the probability P(N) for the system to have N particles has the form, and express \ in terms of 2 and the single-particle partition function Q1- e) [5 pts] Find (N) and (N2) - (N)2 in terms of 2 and Q1.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Physics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats