# UY1: Equation-of-state – Ideal gas law

The equation that relates the pressure P, temperature T and volume V of a gas is called the equation-of-state. In general, the equation-of-state of a gas is complicated. In the limit of low pressure (i.e., low density), the equation-of-state of all gases approach that of the ideal gas.

Ideal Gas

Modelling the behavior of a gas as a collection of particles that obey the laws of classical mechanics.

Assumptions:
– The gas consists of a large number of identical particles that are on average separated by large distances compared with their dimensions. Thus, the particles occupy a negligible fraction of the volume within the container.

– The particles are in a state of random motion and obey Newton’s laws of motion.

– Collisions between the particles themselves and between the particles and the wall of the container are elastic and of negligible duration.

– No long-range forces act on the particles, only short-range repulsive forces act during collisions.

The equation-of state of an ideal gas is found to be:

PV = nRT

,where
P = pressure
V = volume
T = absolute temperature
n = no. of moles of gas (= mass/molar mass)
R = universal gas constant (8.314 J mol-1 K-1

Note: Mole is a counting unit, where one mole = 6.022 x 1023 particles.

P, V, and T are the thermodynamic variables of the gas.

The behaviour of real gases at not-too-high pressures and at not-too-low temperature is very well described by this ideal gas equation.

Another form of ideal gas law

The ideal gas law can also be expressed in number of gas particles N (instead of the number of moles of gas particles n).

PV = NkBT

,where
P = pressure
V = volume
T = absolute temperature
N = number of gas molecules (i.e., number of molecules)
kB = Boltzmann’s constant (1.381 x 10-23 J K-1

Note:
R = NAkB, where NA is the Avogadro’s constant (6.022 x 1023)

Next: Concept Of Kinetic Temperature

Previous: Planck radiation law and Wien displacement law

Back To Thermodynamics

##### Mini Physics

As the Administrator of Mini Physics, I possess a BSc. (Hons) in Physics. I am committed to ensuring the accuracy and quality of the content on this site. If you encounter any inaccuracies or have suggestions for enhancements, I encourage you to contact us. Your support and feedback are invaluable to us. If you appreciate the resources available on this site, kindly consider recommending Mini Physics to your friends. Together, we can foster a community passionate about Physics and continuous learning.

This site uses Akismet to reduce spam. Learn how your comment data is processed.