# Homework Help: Thermal physics - ratio of multiplicites

1. Oct 14, 2007

### solidus_E

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

A penny, made of crystalline copper, is heated at 1,083 degrees celsius and melts. The density of copper is 8.5 g/cm^3. The energy needed to melt copper is 200 J/g. You will need to estimate the volume of a penny.
By what factor does the multiplicity of the copper change when the penny is melted? Express your answer as 10^(some power).

2. Relevant equations

roe = m/v
T (in kelvins) = T (in celsius) + 273.15
q = Em
ln (initial multiplicity / final multiplicity) = q/kT
v = .360 cm^3 (googled, haha)
k = 1.381 x 10^-23 J/K

3. The attempt at a solution

m = (roe)(v) = (8.5 g/cm^3)(0.360cm^3) = 3.06g

q = (200 J/g)(3.06g) = 200 J

ln (ratio of multiplicities) = (200 J) / [(1.4 x 10^-23 J/K)(1356.15 K)] = 3.22 x 10^22

e^ln (ratio of multiplicities) = e^3.22 x 10^22

(from book) e = 10^log(base10)e = 10^0.434

initial multiplicity / final multiplicity = (10^0.434)^(3.22 x 10^22) = 10^(1.4 x 10^22)

So my question is, did I do everything right? Is this the correct answer?

I followed an example used in the book and arrived at this conclusion from it.

Thanks for any help guys.

Last edited: Oct 14, 2007