Question

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

Possible number of ways to a roll 6=5

`S=2.22* 10^(-23)`

Step-by-step explanation:

We are given that two dice are rolled.

There are two possible ways to roll 3:(1,2) and (2,1).

For the outcome of 3 (a particular macrostate) there are 2 microstates.

We have to find the possible number of ways to roll a 6.

We have to find the entropy associated with an outcome of 6.

Possible number of ways to roll 6=(1,5),(5,1),(2,4),(4,2),(3,3)=5

Therefore, possible number of ways to roll 6=5

Entropy associated with an outcome of 6=
`K_bln w`

w=Number of ways

Substitute the value

S=
`1.38* 10^(-23) ln 5`

`S=2.22* 10^(-23)`

Hence, the entropy associated with an outcome of 6=
`S=2.22* 10^(-23)`

Answer 2

The combinations to get a six are 1 and 5, 2 and 4 3 and 3, 4 and 2, and 5 and 1. Thus there ar e5 different ways to roll a 6.
Entropy is associated with the outcome through the formula expressed as S=(kb) ln W substituting, S= (1.38x10-23) ln (5) S= 2.22x10^-23