### Mean Freepath And Non Ideal Gas

**Here’s a summary of the concepts to remember on Mean Free Path and Non-Ideal Gas:**

**Mean Free Path:**

**- Definition:**

- The mean free path of a molecule is the average distance it travels between collisions with other molecules.

**- Inversely proportional relationship:**
-Mean free path is inversely proportional to the density of the gas, meaning as the density of gas particles increases, the mean free path decreases due to more frequent collisions between particles.

**- Importance in Transport Properties:**

- Mean free path is crucial in determining the gas transport properties, influencing factors like viscosity and thermal conductivity.

**- Formula for Ideal Gas:**

- An ideal gas’ mean free path can be calculated using this equation:

$$λ = \frac{k_BT}{\sqrt{2}πd^2P}$$ - Where $$k_B$$ is the Boltzmann constant, $$T$$ is the temperature, $$d$$ is the molecular diameter, and $$P$$ is the pressure.

**Non-Ideal Gas:**

**- Definition:**

- Deviations from the ideal gas behavior characterized by intermolecular interactions.

**- Conditions for Non-Ideal behavior:**

- Non-ideal behavior becomes significant at high pressures and low temperatures.
- This is attributed to intermolecular forces that cause deviations from the ideal gas law’s assumptions.

**- Modeling Non-Ideal Gases:**

- Equations of state like van der Waals and Peng-Robinson equations are used to model non-ideal gas behavior, accounting for these molecular interactions.