using the equation of state pV=nRT ,show that at given temperature density of a gas is proportional to gas pressure p
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Answered by
94
PV=NRT
PV=m/M RT ------ (N=m/M)
PM=m/V RT
PM= DENSITY×RT -- (DENSITY=m/V)
Hence P is directly proportional to density
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Answered by
49
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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