Molecular Kinetic Energy

The Molecular Kinetic Energy calculator computes the kinetic energy of a gaseous molecule based on the temperature (T) and the Boltzmann constant,

INSTRUCTIONS: Choose units and enter the following:

• (T) Temperature of gas.

Kinetic Energy (KE): The calculator returns the kinetic energy in Joules.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Kinetic Molecular Theory formula calculates the average kinetic energy of a gaseous molecule at a specific temperature. The formula for the Kinetic Molecular Theory is:

       KE = 3/2 • k_B • T

where:

• k_B is the Boltzmann constant (1.3806 x 10^-23 m² kg s^-2 K^-1)
• T is the Temperature in Kelvin
• KE is the average kinetic energy of the gaseous molecule. 

Molecular kinetic energies increase when temperature increases, and decrease when temperature decreases. The kinetic energies calculated using this formula are considered to be average kinetic energies because some molecules will be moving faster than others. The only necessary input from the user is the temperature.

Energy Calculators

• Kinetic Energy:                                    `KE= 1/2 *m * v^2`
• Kinetic Energy (change of velocity):    `KE = 1/2*m*(V_1-V_2)^2`
• Relativistic Kinetic Energy:                    `E_K = (m*c^2)/sqrt(1 - v^2"/"c^2") - m*c^2`
• Potential Energy:                                  `U(y) = m*g*y`
• Potential Energy of Gravity (two bodies):   `U(G) = - (G*m1*m2)/r`
• Nuclear Binding Energy:                       `E = m*c^2`
• Quantum Energy (Planck's Equation):   `E = h*f`
• Energy of a Particle in a Box:                `E_n=(n^2h^2)/(8mL^2)`
• Molecular Kinetic Energy:                      `KE = 3/2 * k_B *T`
• Electrostatic Potential Energy:               `E_(el) = k_e * (Q_1*Q_2)/d`
• Photon Energy from Wavelength:          `E = (h*c)/lambda`
• Heat Energy to Change Material Temperature:  `Q = C * m *DeltaT`

Kinetic Energy Calculators

• Kinetic Energy: (KE= ½⋅m⋅v²) Computes the kinetic energy of an object based on its mass and velocity.
• Kinetic Energy from Change in Velocity: KE = ½⋅m⋅(V1-V2)²: Computes the kinetic energy required to change the velocity of a object of a certain mass from an initial velocity to a final velocity.
• Relativistic Kinetic Energy: Computes the kinetic energy of an object accounting for velocities where relativity has a measurable effect
• Molecular Kinetic Energy: Computes the kinetic energy of a gaseous molecule based on the temperature and the Boltzmann constant.

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 429.

Hyper Physics: Kinetic Temperature