Kinetic Theory
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Question : 13
Total: 14
A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called law of atmospheres
n 2 = n 1 exp [ − m g
]
wheren 2 , n 1 h 2 h 1 n 2 = n 1 exp [ − m g N A ( ρ − ρ )
] .
[N A
where
[
Solution:
According to the law of atmospheres,
n 2 = n 1 exp . [ −
( h 2 − h 1 ) ]
wheren 2 , n 1 h 2 and h 1
If we consider the sedimentation equilibrium of suspended particles in a liquid, then in place of mg, we will have to take effective weight of the suspended particles.
Let V = average volume of a suspended particle, r = density of suspended particle,
r′ = density of liquid, m = mass of equal volume of liquid displaced.
According to Archimede’s principle, effective weight of one suspended particle = actual weight – weight of liquid displaced= m g − m ′ g = m g − V ρ ′ g = m g − (
) ρ ′ g = m g ( 1 −
) k B =
where, R is gas constant andN A
Putting,m g ( 1 −
) m g k B n 2 = n 1 exp . [ −
( 1 −
) ( h 2 − h 1 ) ]
where
If we consider the sedimentation equilibrium of suspended particles in a liquid, then in place of mg, we will have to take effective weight of the suspended particles.
Let V = average volume of a suspended particle, r = density of suspended particle,
r′ = density of liquid, m = mass of equal volume of liquid displaced.
According to Archimede’s principle, effective weight of one suspended particle = actual weight – weight of liquid displaced
where, R is gas constant and
Putting,
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