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A gas in equilibrium has uniform density...

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[-(mg)(H_2-H_1)/(kT)]` where `n_2,n_1` refer to number density at heights `h_2` and `h_1` respectively.Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
`n_2= n_1 exp[(-mgN_a)/(RT) (1-(rho)/(rho))(h_2-h_1)]` where `rho` is the density of the suspended particle, and `rho'` that of surrounding medium. `[N_A` is Avogadro's number, and R the universal gas constant].

Answer

Step by step text solution for 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[-(mg)(H_2-H_1)/(kT)] where n_2,n_1 refer to number density at heights h_2 and h_1 respectively.Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: n_2= n_1 exp[(-mgN_a)/(RT) (1-(rho)/(rho))(h_2-h_1)] where rho is the density of the suspended particle, and rho' that of surrounding medium. [N_A is Avogadro's number, and R the universal gas constant]. by PHYSICS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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Knowledge Check

  • The density of the ideal gas is given by

    A
    `d=(PM)/(RT)`
    B
    `d=(RT)/(PM)`
    C
    `d=(PR)/(TM )`
    D
    `d=(PT)/(RM)`
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