## 8.27 Boltzmann Equation Question

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Denise 3L
Posts: 13
Joined: Fri Sep 26, 2014 2:02 pm

### 8.27 Boltzmann Equation Question

I'm trying to calculate the residual molar entropy of this problem using S=klnW, but when I plug in the numbers
(1.38[*]10^-23 JK^-1) ln(6^6.02*10^23)
My calculator gives me an overflow error?

Niharika Reddy 1D
Posts: 127
Joined: Fri Sep 26, 2014 2:02 pm

### Re: 8.27 Boltzmann Equation Question

Properties of logs allow you to bring the exponent (Avogadro's number in this case) to the front and multiply it after taking the natural log of the base (6). Since the equation is S=klnW, and W=6^(6.022x10^23=NA), you can bring NA down to the front of the expression. This gives S=NAkln6=14.9J/K. As a side note, NAk equals the gas constant R, in the form 8.3145 J/K•mol. So you can also simplify the calculation by saying S=Rln6

The calculator will be able to handle the expression if you bring the exponent of the base of the log down to the front.

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