# The Boltzmann constant

N – # of particlesN!(total spaces)W = # of accessibleW =microstatesno!n1!n2!n3! …(multiplicity)n, = # of particles with iunits of energy (tokens)So the entropy isS = k In W = k In30!no!n1!n2!n3!”..The Boltzmann constant is 1.38 x 10-23 J/KCase 1: Arrange the tokens so that there is just one on every square of the grid. Calculatethe multiplicity (W), the entropy divided by the Boltzmann constant (S/k) and entropy (S) ofthis very unlikely situation (where n1 = 30 and all of the other n; = 0):W=S/k =S =J/KCase 2: Arrange the tokens so that all 30 are on a single square of the grid. Calculate boththe multiplicity and the entropy divided by the Boltzmann constant and entropy of this veryunlikely situation (where no = 29, n30 = 1 and all of the other n; = 0):W =S/k =S=J/KCase 3: Use the dice to randomly place the 30 tokens onto the grid.Penny#Place penny on square1W N145091042111610792923121716292316282018221917207215221623112423252826122724281229303020According to the list placing pennies on the grid until all 30 pennies are gone. Record thedistribution numbers (no, nj, etc.) and calculate both the multiplicity and the entropydivided by the Boltzmann constant and entropy of this situation:n3 =no =n1 =n2=n4 =ns =n6 =n7 =ng =ng =n10 =n1 =W =S/k =S =J/K

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