Respuesta :
Answer:
[tex]5.31\times 10^{-19}[/tex]
Explanation:
Entropy of the system, [tex](S) = - k_{B} lnW[/tex]
[tex]k_{B}[/tex] is Boltzmann constant, W is the number of microstates
[tex]p_{i}[/tex] is the probability of a molecule in a given energy level. [tex]p_{i} =\frac{N_{i} }{N}[/tex]
[tex]{N_{i} }[/tex] = number of molecules in a energy state, N = total number of molecules
And,
[tex]ln W = - N \sum p_{i} lnp_{i}[/tex]
In the given problem
[tex]N = 100000+10000+1000 = 111000[/tex]
[tex]p_{1} = 100000/111000 = 0.9009[/tex]
[tex]p_{2} = 10000/111000 = 0.09009[/tex]
[tex]p_{3} = 1000/111000 = 0.009009[/tex]
then,
[tex]S = - N k_{B} [p_{1} lnp_{1} + p_{2}lnp_{2} + p_{2}lnp_{2}][/tex]
Therefore,
[tex]S = - Nk_{B} [ 0.9009ln0.9009 + 0.09009ln0.09009 + 0.009009ln0.009]\\S== -111000\times 1.38\times10^{-23}[ - 0.9009\times 0.1 - 0.09009\times 2.41 - 0.009009\times 4.71]\\S= 111\times 1.38\times 10^{-20} [ 0.09009 + 0.217+0.04243]\\S= 151.8\times 10^{-20}\times 0.34952\\S=53.06\times 10^{-20} JK^{-1} \\S=5.31\times 10^{-19} JK^{-1}[/tex]
Therefore entropy of the system is [tex]5.31\times 10^{-19}[/tex]
