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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=?

Respuesta :

meerkat18

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
lublana

Answer:

Possible number of ways to a roll 6=5

[tex]S=2.22\times 10^{-23}[/tex]

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=[tex]K_bln w[/tex]

w=Number of ways

Substitute the value

S=[tex]1.38\times 10^{-23} ln 5[/tex]

[tex]S=2.22\times 10^{-23}[/tex]

Hence, the entropy associated with an outcome of 6=[tex]S=2.22\times 10^{-23}[/tex]

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