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13 January, 13:19

Prove that density of an ideal gas is proportional to pressure dont spam give right derivation

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  1. 13 January, 13:37
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    The density of an ideal gas is proportional to its pressure through ideal gas equation in the mentioned below steps.

    Explanation:

    For an ideal gas, we know that pV=nRT

    where p = pressure of the gas

    V-volume of the gas

    n - no of moles of the gas in consideration

    R = Gas constant

    T = temperature of the gas

    Thus

    pressure (p) = nRT/V - - equation 1

    we know that no of moles of any gas = mass of the gas (m) / Molar mass of the gas (M)

    Putting the value of n in the equation 1

    p = mRT/MV - - equation 2

    We know that density (ρ) = mass/volume

    equation 2 can be re-arranged as

    p=RT. m/V. M

    Substituing, m/v in equation 2 by density (ρ)

    p=ρRT/M - -equation 3

    Equation 3 can be re-written as

    ρ=pM/RT

    where

    ρ = density of the gas concerned

    p=pressure of the gas

    M=molar mass of the gas

    R = Gas constant

    T = Temperature of the gas concerned

    Hence in the final equation density of the gas is directly proportional to the pressure
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