Entropia de mistura

Entropy of mixing

CY101 T. Pradeep 2007

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The meaning of entropy: Entropy of mixing
Consider that a number of ideal gases are separated which are present in a vessel. Let ni be the number of moles of each gas and Vi is the volume it occupies. The total entropy,
S1 = ∑ni (Cv ln T + R ln Vi + Si) 1
Note the term Si. It is because, dS = Cv(dT/T) + R(dV/V)
S = Cv ln T + R ln V + So
Let the partitions between the gases are removed and they are allowed to mix. Let the volume the gases occupy is V. The entropy,
S2 = ∑ni (Cv lnCY101 T. Pradeep+ Si) 2
T + R ln V 2007

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Assume that the pressure has not changed and there is no change in temperature. Ratio of volume,
Vi/V = ni/n = Xi - the mole fraction.
Where n is the total number of moles.
Substituting Vi = VXi in Eqn.1
S1 = ∑ni (Cv ln T + R ln V + R ln Xi + Si)
The increase in entropy, the entropy of mixing,
S2 – S1 = –∑ ni R ln Xi
Entropy of mixing of 1 mole of the ideal gas,
∆Sm = – R ∑ni/n ln Xi = –R ∑ Xi ln Xi
The fraction Xi is less than unity in all cases, the logarithm is negative and thus ∆Sm is always positive.
Thus mixing of gases (eg. by diffusion), always results in increase in entropy. Mixing is spontaneous!
This is in general true CY101 T. Pradeep 2007 liquid or solid. of any material,

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Entropy and disorder
Spontaneous processes net increase in entropy randomness of distribution (mixing).

increase in

The diffusion of initially separated gases result in an increase in entropy. The process has increased the random distribution of molecules. Spontaneous conduction of heat results in the random distribution of kinetic energy of the atoms. Thus spontaneous processes increase randomness, at the same time increases entropy. Therefore, it is appropriate to suggest a relationship between entropy and randomness.
CY101 T. Pradeep 2007

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This definition of entropy, that it is a measure of randomness, is one of great value. Apart form the