Understanding the Partition Function of a Mixture in Statistical Mechanics

In statistical mechanics, the partition function plays a crucial role in determining the thermodynamic properties of a system. Let's explore how the partition function of a mixture can be expressed in terms of the single-particle partition functions of its components.

Expressing the Partition Function Z of the Mixture

The partition function of a mixture is expressed as Z = NA * qA * NB * qB, where:

• Z is the total partition function of the mixture.
• NA is the number of particles of type A in the mixture.
• qA is the single-particle partition function for particles of type A.
• NB is the number of particles of type B in the mixture.
• qB is the single-particle partition function for particles of type B.

Explanation of the Expression

The expression Z = NA * qA * NB * qB signifies the total partition function for a system containing NA particles of type A and NB particles of type B. Each individual particle contributes multiplicatively to the total partition function, considering all possible states accessible to them.

Here, qA and qB represent the sum of the statistical weights of all states accessible to a single particle of type A and B, respectively, weighted by the Boltzmann factor.

Express the partition function Z of the mixture in terms of the single-particle partition functions of A and B.

Final answer: The partition function of a mixture is expressed as Z = NA * qA * NB * qB in statistical mechanics, where qA and qB are the single-particle partition functions for particles A and B respectively. Therefore, the correct option is A.

Explanation: The partition function Z of the mixture can be expressed in terms of the single-particle partition functions of A and B. In statistical mechanics, each individual particle contributes multiplicatively to the total partition function (also known as summation over states). In this case, the correct expression would be Z = NA * qA * NB * qB.

Here, qA and qB are the single-particle partition functions for particles A and B respectively. They represent the sum of the statistical weights of all states accessible to a single particle, weighted by the Boltzmann factor.

To summarize, the correct answer is option A: Z = NA * qA * NB * qB.