# Particle Velocity Calculator, Formula, Calculation With Example

### Particle Velocity Calculator:

Particle Velocity Calculator helps calculate the average velocity of gas particles. All you need to know is the temperature of the gas and the mass of its particles. Average speed is one of the information in the Maxwell-Boltzmann distribution. Read on to know particle velocity definition, formula, procedure to calculate average velocity of gas particles etc.

Additionally, the Maxwell-Boltzmann Distribution is clearly explained with its formula.

Particle velocity is defined as the speed of a particle in a medium when it transmits a wave. It is also known as Maxwell-Boltzmann equation or distribution.

### Particle Velocity Formula:

Particle velocity of average velocity particle V(m/s) in meter per second is equal to the eight and multiply the the Boltzmann constant K(j/k) in joule per kilo and multiply the temperature of the gas  T(0c )  in degree Celsius and divided by pi π value in 3.14 and multiply the mass m (kg) in kilogram and multiply the one divided by two (1/2).Hence the particle velocity calculator can be written as

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V(m/s)=(8 * K(j/k) * T(0c )  /π * m (kg)) ^ (1/2)

### Maxwell –Boltzmann Distribution:

F(v)=(m / 2 * π * K *T) ^ (3/2) * 4 π * V2 *Exp(-m *V2 /(2* K *T )

Where m is mass of the particle

T= is the temperature of the gas

V=is the velocity

K=is the Boltzmann constant and k=1.3806 *10 ^ (-23 ) J /K

According to Newton’s equations of motion, particles in a gas move and collide with each other. However, Avogadro’s number of order 10^23 makes it impossible to detect particle motion. Therefore, we use temperature to describe gas particles.

### Average velocity of a particle:

(8 * K *T /π * m) ^ (1/2)

According to the Maxwell-Boltzmann equation we can get formula for Average velocity of a particle in gas.

Where K= is the Boltzmann constant

T=is the temperature

M=is the mass of particles

Is the average or mean speed

### Example:1

Calculate the mass 25 gram and temperature 560 c and find the velocity value?

Mass=25 kg

Temperature =56 c

Convert mass 25 kilo- gram into gram

Mass =25000.0 g

Convert temperature 56 celsius into Kelvin

Temperature =329.15 k

<v>=(8 * K *T / (π * m )^ (1 /2 )

K=1.3806 *10 ^ (-23 ) J/K is the Boltzmann constant

<v>=(8 * K *T / (π * m )^ (1 /2 )

<v>=(8* 1.3806 *10 ^ (-23 ) * 329.15  k / (3.14 * 2500.0 kg )^ (1/2)

V=2.1514483136 *10-11  m/s

### Example:2

Calculate the mass 9  gram and temperature 380 c and find the velocity value?

Mass=9 kg

Temperature =38 c

Convert mass 9 kilo- gram into gram

Mass =9.0 g

Convert temperature 38 celsius into Kelvin

Temperature =311.15  k

<v>=(8 * K *T / (π * m )^ (1 /2 )

K=1.3806 *10 ^ (-23 ) J/K is the Boltzmann constant

<v>=(8 * K *T / (π * m )^ (1 /2 )

<v>=(8* 1.3806 *10 ^ (-23 ) * 311.15  k / (3.14 * 9.0  kg )^ (1/2)

V=1.102472 *10-09 m/s