Science > Physics > Kinetic Theory of Gases > Pressure Exerted by Gas

In this short article, we shall examine to derive an expression for pressure exerted by gas on the wall surfaces of container. We shall additionally derivation of various gas regulations utilizing the kinetic theory of gases.

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Let usthink about a gas enclosed in a cube whose each edge is of size ‘l’. LetA be the location of each confront of the cube. So A= l². Let V bethe volume of the cube (or the gas). SoV = . Let ‘m’ be the massof each molecule of the gas and ‘N’ be the full variety of molecules of the gasand also ‘M’ be the full mass of the gas. So M = mN.

Suppose thatthe 3 intersecting edges of the cube are alengthy the rectangular co-ordinateaxes X, Y and Z through the origin O at one of the corners of the cube. Bythe kinetic theory of gases, we recognize that molecules of a gas are in a state ofrandom activity so it deserve to be imagined that on an average N/3 molecule areconstantly relocating parallel to each edge of the cube i.e. alengthy the co-ordinateaxes. Let velocities of N/3 molecules moving parallel to X-axis be C1,C2, C3, …. , CN/3 respectively.

Consider a molecule relocating via the velocityC1in the positive direction of the X-axis. The initial momentum of the molecule,

p1 =mC1,

It will collide normally with the wall ABCD and as the collision is perfectly elastic rebounds through the very same velocity. Hence, momentumof molecule after collision,

p2 = – mC1

Change in the momentum of the moleculeas a result of one collision via ABCD

Δp = p2 – p1

Δp = – mC1 – mC1 =– 2 – mC1

Before the following collision with the wall ABCD the molecule will travel a distance 2l via velocity C1. So time interval in between two successive collisions of the molecule with ABCD= 2l /C1

Number of collisions of the molecule per unit with wallABCD= C1/ 2l

Changein the momentumof the moleculeper unit time

= – 2mC1× C1/ 2l =– mC1² /l

But by Newton’s second law we recognize that the rate of readjust of momentum is equal to the impressed force.

So force exerted on the molecule by wall ABCD=-mC1²/l

From Newton’s 3rd law of motion, action and reactivity are equal and oppowebsite. So force exerted on the moleculeby wall ABCD =mC1² /l. Hence eincredibly molecule will exert a force on the wall ABCD. So total force exerted on the wall ABCD due to molecules relocating in the positive X-axis direction is offered by


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The pressure exerted on each wall will certainly be the exact same and i.e. equal to the press of the gas. By definition of r.m.s. velocity


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This is an expression for pressure exerted by a gas on the wall surfaces of the container.

Boyle’s Law from Kinetic Theory of Gases:

Statement:

The temperature remaining constant the pressure exerted by acertain mass of gas is inversely proportional to its volume.


Explanation:

If P is the pressure and also V is the volume of a specific mass of enclosed gas, then

P∝1 / V ∴ P V = constant

Proof:

From kinetic theory of gases, the push exerted by a gas is given by


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Wright here M = Total mass of the gas = Nm

V = Volume of the gas

ρ= Density of the gas

C̅ = r.m.s. velocity of gas molecules.

M = Molecular mass of the gas


N = Number of molecules of a gas

m = Mass of each molecule of a gas.

But by assumptions of the kinetic concept of gases the average kinetic energy of a molecule is consistent at a continuous temperature. Thus the right-hand side of the equation is consistent.

Therefore, PV =constanti.e. P∝1 / V . This is Boyle’s Law.

Therefore Boyle’s law is deduced from the kinetic concept ofgases.

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Relation Between r.m.s. Velocity of Gas Molecule and also the Absolute Temperature of the Gas:

From kinetic concept of gases, the press exerted by a gas is provided by


Wbelow M = Total mass of the gas = Nm

V = Volume of the gas

ρ= Density of the gas

C̅ = r.m.s. velocity of gas molecules.

M = Molecular mass of the gas

For one mole of a gas, the full mass of the gas can betaken as molecular weight