1. What is the Pressure of Gas using Number Density Formula?

The pressure of gas using number density formula calculates the pressure exerted by a gas based on its number density and temperature, using the ideal gas law at the molecular level with Boltzmann's constant.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P_{gas} \) — Pressure of gas (Pascal)
• \( n \) — Number density (particles per cubic meter)
• \( [BoltZ] \) — Boltzmann constant (1.38064852 × 10⁻²³ J/K)
• \( T_g \) — Temperature of gas (Kelvin)

Explanation: This formula derives from the ideal gas law, connecting microscopic properties (number density) with macroscopic measurements (pressure).

3. Importance of Pressure Calculation

Details: Accurate pressure calculation is essential for understanding gas behavior in various systems, from industrial processes to atmospheric studies and vacuum technology.

4. Using the Calculator

Tips: Enter number density in particles per cubic meter and temperature in Kelvin. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is number density?
A: Number density represents the number of particles per unit volume, typically measured in particles per cubic meter.

Q2: Why use Boltzmann's constant?
A: Boltzmann's constant connects the microscopic world of individual particles with macroscopic thermodynamic quantities like temperature and pressure.

Q3: What are typical pressure values?
A: Atmospheric pressure is approximately 101,325 Pa. Vacuum systems can range from 10³ to 10⁻¹² Pa depending on the application.

Q4: When is this formula applicable?
A: This formula works well for ideal gases at moderate temperatures and pressures where intermolecular forces are negligible.

Q5: How does temperature affect pressure?
A: Pressure is directly proportional to temperature when number density remains constant (Gay-Lussac's law).