1. What is the Pressure of Gas Formula?

The pressure of gas formula calculates the pressure exerted by gas molecules in a 3D container based on kinetic theory. It relates pressure to the number of molecules, their mass, root mean square speed, and the volume of the container.

2. How Does the Calculator Work?

The calculator uses the pressure formula:

Where:

• \( P_{gas} \) — Pressure of gas (Pascal)
• \( N_{molecules} \) — Number of molecules
• \( m \) — Mass of each molecule (kg)
• \( C_{RMS} \) — Root mean square speed (m/s)
• \( V_{gas} \) — Volume of gas (m³)

Explanation: The formula derives from kinetic theory, where pressure results from molecular collisions with container walls.

3. Importance of Pressure Calculation

Details: Accurate pressure calculation is essential for understanding gas behavior, designing containers, and various engineering applications involving gases.

4. Using the Calculator

Tips: Enter number of molecules, mass per molecule in kg, root mean square speed in m/s, and volume in m³. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is root mean square speed?
A: Root mean square speed is the square root of the average of the squares of the speeds of all molecules in the gas.

Q2: Why is there a 1/3 factor in the formula?
A: The 1/3 factor accounts for the three-dimensional nature of the container and equal distribution of molecular motion in all directions.

Q3: What units should be used for input values?
A: Use SI units: molecules (count), kg for mass, m/s for speed, and m³ for volume to get pressure in Pascals.

Q4: Does this formula work for ideal gases only?
A: Yes, this formula is derived for ideal gases that follow kinetic theory assumptions.

Q5: How does temperature relate to this formula?
A: Temperature is related through the root mean square speed, as \( C_{RMS} = \sqrt{\frac{3kT}{m}} \), where k is Boltzmann's constant.