First slide

Calculation of pressure

Question

1 mole of an ideal gas is contained in a cubical volume 'V'. ABCDEFGH at 300k. One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At a given time

Moderate

A

the pressure on EFGH would be zero.
B

the pressure on all the faces will be equal.
C

the pressure on EFGH would be double the pressure on ABCD
D

the pressure on EFGH would be half that on ABCD.

Solution

For large number of molecules whose motions are completely at random, u_x = u_y = u_z = u/√3
where u = RMS velocity.
It m be the mass of each molecule, N = total number of molecules, Then
${P_{ABCD}} = {P_{yz}} = \frac{{zm\,\,{u_y} \times N}}{{{l^2} \times \frac{{2l}}{{4x}}}} = \frac{{\left( {mN} \right)4_x^2}}{{{l^3}}}$
$= \rho u_x^2 = \frac{{\rho {u^2}}}{3}$
${P_{EFGH}} = {P_{xy}} = \frac{{m\,{u_z} \times N}}{{{l^2} \times 2l/{u_2}}} = \frac{{\left( {mN} \right)u_z^2}}{{2{l^3}}}$
$= \frac{1}{2}\rho \frac{{{u^2}}}{3}$
$\therefore {P_{EFGH}} = \frac{1}{2}{P_{ABCD}}.$

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