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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

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the pressure on EFGH would be zero.

the pressure on all the faces will be equal.

the pressure on EFGH would be double the pressure on ABCD

the pressure on EFGH would be half that on ABCD.

answer is D.

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Detailed Solution

For large number of molecules whose motions are completely at random, u_x = u_y = u_z = u/√3

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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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