(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Problem-5: In the class we saw that property of additivity of the entropy for systems in thermalcontact relies on the approximation that we compute entropy of the most probable state ln(g1g2)maxinstead of full ln g(N,U) = ln(P,U1)

g(N1,U1)g(N2,U −U1)). The error made turns out to be really

small provided that each systems contains large number of particles. For the example of spins with

N1 = N2 = N/2 >> 1 we found

ln g(N, s) = ln(g1g2)max +1/2ln(N/8).

(4)

Consider now a special case when one system is large having N1 = 10E22 spins but the other is relatively

small with only N2 = 10 spins. Take s = 0 and compute the relative error in the definition

of entropy. Is it still a good idea to use such definition of entropy when N1 >> N2? [1 pt]

2. Relevant equations

3. The attempt at a solution

Ok so I honestly haven't a clue where to start I am just looking for type of guidance. My first idea would be to find g1 and g2 then from there I am totally lost.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Relative error definition of entropy

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**