The best method for the separation of naphthalene and benzoic acid from their mixture is sublimation.

Sublimation is the process in which a solid substance directly converts into vapor or gas without going through the liquid phase. It is based on the principle that different substances have different sublimation temperatures. In the case of naphthalene and benzoic acid, their sublimation temperatures are significantly different, making sublimation an effective method for their separation.

Explanation:

1. Sublimation:
- Sublimation is the process in which a solid substance directly converts into vapor or gas without going through the liquid phase.
- It is based on the principle that different substances have different sublimation temperatures.
- In the case of naphthalene and benzoic acid, their sublimation temperatures are significantly different.

2. Naphthalene and Benzoic Acid:
- Naphthalene is a solid aromatic hydrocarbon that forms white crystals and has a characteristic odor.
- Benzoic acid is a white crystalline solid that is slightly soluble in water and has a strong, sweet odor.

3. Sublimation Temperatures:
- The sublimation temperature of naphthalene is around 80 degrees Celsius.
- The sublimation temperature of benzoic acid is around 120 degrees Celsius.

4. Separation Process:
- The mixture of naphthalene and benzoic acid is heated gently.
- The heat causes naphthalene to sublime at its lower sublimation temperature of 80 degrees Celsius.
- The naphthalene vaporizes and can be collected separately.
- Since benzoic acid has a higher sublimation temperature of 120 degrees Celsius, it remains as a solid.

5. Collection of Components:
- The naphthalene vapor is collected and condensed back into solid form by cooling.
- The benzoic acid, which remains as a solid, can be easily separated from the mixture by physical means such as filtration or by simply decanting the liquid.

Advantages of Sublimation:
- Sublimation is a simple and effective method for separating mixtures of solids.
- It does not involve the use of solvents or chemicals, making it a relatively clean and environmentally friendly process.
- It allows for the recovery of both components in their pure form.

Therefore, sublimation is the best method for the separation of naphthalene and benzoic acid from their mixture due to the significant difference in their sublimation temperatures.