There is a mixture of two kinds of atoms A and B. the number of the atoms A, B i

Question

There is a mixture of two kinds of atoms A and B. the number of the atoms A, B is Ng, respectively. the total number of atoms is N = N_A + N_B. the Helmholtz free energy of the mixture is F and we define f = F/N to be the free energy per atom. Defining x = N_B/N Ng/N the ratio of the number of B, we have the following graph of the free energy per atom for a homogeneous mixture at temperature T. the tangents at x = 0.25 and 0.7 are the same horizontal line. What kind of physical state does the mixture take at x = 0.25 and 0.7, respectively? Explain the reason. What kind of physical state does the mixture take at x= 0.5? Explain the reason. You can represent the results in fraction.

Explanation / Answer

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(1) This tangent denotes the lowest free enrgy state that is obtained only by drawing the lowest possible straight line that has two points and which tells us about the achievement of diffusive equilibrium between two atoms i.e.

chemical potential of A=chemical potential of B

(2) This denotes the unstable state. In this state, we get inhomogeneous mixture of two atoms.there is no thermodynamic barrier to the growth of a new phase in this region.

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