Question

Prove pressure of a gas is directly proportional to the density of gas

Answer 1

At a given temperature and at atmospheric pressure, solids and liquids will have a specific volume. By increasing the pressure on the material, you can often slightly decrease its volume and thus increase its density.

The equation of state is given by, pV = nRT ……….. (i)

Where, p → Pressure of gas

V → Volume of gas

n→ Number of moles of gas

R → Gas constant

T → Temperature of gas

From equation (i) we have,

p = n RT/V

Where n= Mass of gas(m)/ Molar mass of gas(M)

Putting value of n in the equation, we have

p = m RT/ MV ------------(ii)

Now density(ρ) = m /V ----------------(iii)

Putting (iii) in (ii) we get

P = ρ RT / M

OR

ρ = PM / RT

Hence, at a given temperature, the density (ρ) of gas is proportional to its pressure (P)

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