Question

I think i have an idea of this, but I am not sure.

With two dice, each numbered 1-6, there are two possible ways to roll a 3: Thus, for the outcome of 3 (a particular macrostate) there are 2 microstates. How many possible ways are there to roll a 6?

What is the entropy associated with an outcome of 6?
S=?

Answer 1

1,5; 2,4; 3,3 x2 for each die

so there are 6 ways (microstates)

Answer 2

Yeah I was pretty sure about that. I was confused on the entropy associated with an outcome of 6?

Answer 3

I think they want you to use \( S= k_B* ln(W) \)

Answer 4

There are only 5 microstates, because (3,3) must be counted only once.

Answer 5

are you sure? is it because the order is unimportant? why wouldn't the other combinations (1, 2 and 2, 4) fall under the same category?

Answer 6

x,y and y,x correspond to 2 different results with dice A and dice B.
A=x B=y OR A=y,B=x

x,x is unique: A=B=x

Answer 7

thanks for clearing that up, sir.

Answer 8

yes it was 5 for the first part.
then the second had to use S=KlnW.
K = 1.23x10^-23 w equals the micro state. so 5 for 6.
that equals 2.22*10^-23