# 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.

Useful java applet on ideal gas model: Click

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)

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