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We have a system A with 8 particles and a total energy of 4 units. Each...

We have a system A with 8 particles and a total energy of 4 units. Each particle is allowed to have an energy of either 0 or 1 units only. What is the multiplcity of this system W? What is the value of S/kB= lnW?

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Expert Solution

In statistical thermodynamics, multiplicity W, from the German Wahrscheinlichkeit (war-shine-leash-kite), meaning probability, is the number of quantum states associated with one particular macroscopic thermodynamic state, defined typically by two state parameters, such as volumeand energy, of a Boltzman-type system, containing a larger number of particles N, with non-correlated velocities. In simpler terms, W is the number of different ways P particles can be distributed in a system composed of N different, but connected, compartments

From the given data is clear that there are 2 sets of particles, 1 set of particle having 0 energy another set having 1 unit energy, therefore it can be considered as 4 and 4.

W= 8!/(4! 4!) = 70

S/kB= lnW

lnW= 6.022*1023*logW

kB=1.3*10-23

S= 15.33

queen_honey_blossom answered 2 years ago
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