Boltzmann Constant Formula: Definition And Applications

Boltzmann constant formula

The physical constant relates the average kinetic energy of gas particles to the temperature of the gas, which is represented by k or kB in thermodynamics. As observed in Boltzmann’s entropy formula and Planck’s law of black body radiation, the Boltzmann constant is measured as J/K or m2Kgs-2K-1.

Boltzmann Constant Definition

The energy of a gas molecule is proportional to the absolute temperature in most cases. When a gas is heated, the molecules in it move faster. The kinetic energy per molecule increases as the temperature increases. As a result, either a higher pressure or an increased volume will result if the gas is contained within a constant volume space.

The Boltzmann constant, k, is of physical significance as it measures the energy (heat) assigned to the random thermal motions of a material’s particles. 

Also Check – Malic Acid Formula

For example, the average energy per degree of freedom in a classical system in equilibrium at temperature T is kT/2. Taking one atom as an illustration, with three translational degrees of freedom (i.e. able to move in either the x, y or z-direction), and considering a gas made up of N non-interacting atoms; then its total thermal energy can be derived as 3NkT/2.

Also Read : Surface Chemistry Formula

Value Of Boltzmann Constant

Gas constant R is divided by Avogadro’s number NA to obtain Boltzmann constant values. The value of k is

Boltzmann constant, kB= 1.3806452 × 10-23J/K

Boltzmann’s Constant

Everything in this world is made up of atoms and molecules. Put a vessel full of water on fire, lid it with a lid, and remove the lid before it boils. When we put our hand over the steaming vessel, it feels hot. Why? The steam comprises randomly moving particles that strike your hand with high kinetic energy. According to Boltzmann’s idea, this kinetic energy comprises the (water) molecules’ kinetic energy. The higher the temperature, the more entropy these particles have, and hence, the greater is the transfer of energy to your hand, which makes you feel hotter faster. In conclusion, when large amounts of particles hit our skin at a very high speed, they transmit kinetic energy and cause our hands to get burnt due to more molecules circling our skin. This was an average molecular explanation for how temperature works.

Also Check – Value of Gas Constant Formula

Boltzmann’s Constant Formula

Consider an ideal gas equation: 

   PV = nRT  (Universal gas law)       

Where P is the Pressure in Pascals         

V is the Volume in Metre cubes         

n  = no of moles of the gas         

R = The gas constant         

T = Temperature in Kelvin

Also Check – Monatomic Gases Formula 

Applications Of Boltzmann’s Constant

• To express the energy partition of an atom in classical statistical mechanics, the Boltzmann Constant is used. 
• In semiconductor physics, it is used to express thermal voltage. The statistical definition of entropy is used to express the Boltzmann factor.
• It calculates the quantity of heat emitted by the dark body. 
• It converts temperature (K) into intensity (Wm-2), essentially power per unit area.

Facts About Boltzmann’s Constant

• The Boltzmann Constant, named after Austrian physicist Ludwig Boltzmann and proposed by Max Planck, is a key tool in classical statistical mechanics for expressing the equipartition of energy in an atom. 
• Furthermore, it also demonstrates the relationship between energy and temperature and is used to study heat. Its dimensions are [M1L2T-2K-1], with a value of 1.3806452 x 10-23J/Kand 8.6173303 x 10-5 eV/K in eV. 
• This constant plays a major role in semiconductor physics’ statistical definition of entropy and thermal voltage.