Particle Velocity Calculator

Particle Velocity Calculator:

Enter the values of temperature, T_(K)­ and mass of gas particle, m_(kg) to determine the value of particle velocity, v_(m/s).

Enter Temperature :		K
Enter Mass of the Gas Particles :		kg
Result – Particle Velocity :		m/s

Particle Velocity Formula:

Particle velocity, often referred to as the root-mean-square speed, is a measure of the speed of particles in a gas that is derived from the kinetic theory of gases.

Particle velocity, v_(m/s) is calculated by dividing the squareroot of Boltzmann constant, k (1.38 * 10^-23 J/K), temperature, T_(K)­ in Kelvin and 8 by pi and mass of gas particle, m_(kg) in kilograms.

Particle velocity, v_(m/s) = √ ( 8 * k * T_(K) / 3.14 * _­ m_(kg) )

v_(m/s) = particle velocity in metres per second, m/s.

k = Boltzmann constant (1.38*10^-23JK)

T_(K) = temperature in Kelvin, K.

m_(kg) = mass of the gas particles in kilograms, kg.

Particle Velocity Calculation:

1.Calculate the particle velocity for hydrogen molecules at a temperature of 300 K. Assume the mass of a hydrogen molecule (H₂) is approximately 3.32×10^-27kg.

Given: k = 1.38*10^-23JK, T_(K) = 300K, m_(kg) = 3.32 * 10^-27.

Particle velocity, v_(m/s) = √ ( 8 * k * T_(K) / 3.14 * _­ m_(kg) )

v_(m/s) = √ ( 8 * 1.38 * 10^-23 / 3.14 * 3.32 * 10^-27 )

v_(m/s) = √ 3.168 * 10⁶

v_(m/s) = 1782.42m/s.

2.Suppose you have a gas particle moving at a velocity of 500 m/s at a temperature of 300 K. The Boltzmann constant is 1.38×10^-23. Find the mass of the gas particle.

Given: k = 1.38*10^-23JK, T_(K) = 300K, v_(m/s) = 500m/s.

Particle velocity, v_(m/s) = √ ( 8 * k * T_(K) / 3.14 * _­ m_(kg) )

m_(kg) = 8 * k * T_(K) / 3.14 * v²_(m/s)

m_(kg) = 8 * 1.38 * 10^-23 300 / 3.14 * 500²

m_(kg) = 3.312 * 10^-20 / 785397.5

m_(kg) = 4.217 * 10^-26.