Pressure of an Ideal Gas (Kinetic Theory)

📊 advanced

$$P = \frac{1}{3} \frac{Nm\bar{v^2}}{V}$$

Relates the microscopic motion of gas molecules to the macroscopic pressure.

Variables & Units

$N$

Number of molecules

Unit: Count

$m$

Mass of one molecule

Unit: $kg$

$\bar{v^2}$

Mean square speed

Unit: $m^2/s^2$

Key Information

📐 Derived From

Statistical mechanics and impulse-momentum theorem.

💡 Example

Explaining why increasing temperature increases pressure.

🔧 Applications

Vacuum physics and aerospace engineering.

⚠️ Constraints

Assumes elastic collisions and no intermolecular forces.

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