Agas in equilibrium has uniform density and pressure throughout itsvol

1.	Agas in equilibrium has uniform density and pressure throughout itsvolume. This is strictly true only if there are no externalinfluences. A gas column under gravity, for example, does not haveuniform density (and pressure). As you might expect, its densitydecreases with height. The precise dependence is given by theso-called law of atmospheresn2= n1exp [-mg(h2–h1)/kBT]Wheren2,n1refer to number density at heights h2and h1respectively. Use this relation to derive the equation forsedimentation equilibrium of a suspension in a liquid column:n2= n1exp [-mg NA(ρ- P′)(h2–h1)/(ρRT)]Whereρ is the density of the suspended particle, and ρ’ thatof surrounding medium. [NAis Avogadro’s number, and Rtheuniversal gas constant.] [Hint:Use Archimedes principle to find the apparent weight of the suspendedparticle.]
Answer» 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 n₂ = n₁ exp [-mg (h₂– h₁)/ k_BT] Where n₂, n₁ refer to number density at heights h₂ and h₁ respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: n₂ = n₁ exp [-mg N_A(ρ - P′) (h₂ –h₁)/ (ρRT)] Where ρ is the density of the suspended particle, and ρ’ that of surrounding medium. [N_A is Avogadro’s number, and R the universal gas constant.] [Hint: Use Archimedes principle to find the apparent weight of the suspended particle.]

Agas in equilibrium has uniform density and pressure throughout itsvolume. This is strictly true only if there are no externalinfluences. A gas column under gravity, for example, does not haveuniform density (and pressure). As you might expect, its densitydecreases with height. The precise dependence is given by theso-called law of atmospheresn2= n1exp [-mg(h2–h1)/kBT]Wheren2,n1refer to number density at heights h2and h1respectively. Use this relation to derive the equation forsedimentation equilibrium of a suspension in a liquid column:n2= n1exp [-mg NA(ρ- P′)(h2–h1)/(ρRT)]Whereρ is the density of the suspended particle, and ρ’ thatof surrounding medium. [NAis Avogadro’s number, and Rtheuniversal gas constant.] [Hint:Use Archimedes principle to find the apparent weight of the suspendedparticle.]

Answer»

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

n₂
= n₁
exp [-mg
(h₂–
h₁)/
k_BT]

Where
n₂,
n₁
refer to number density at heights h₂
and h₁
respectively. Use this relation to derive the equation for
sedimentation equilibrium of a suspension in a liquid column:

n₂
= n₁
exp [-mg N_A(ρ
- P′)
(h₂
–h₁)/
(ρRT)]

Where
ρ is the density of the suspended particle, and ρ’ that
of surrounding medium. [N_A
is Avogadro’s number, and R
the
universal gas constant.] [Hint:
Use Archimedes principle to find the apparent weight of the suspended
particle.]

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