First slide

Calculation of pressure

Question

A molecule of gas collides with the wall of a container elastically.
The expression of total pressure to the group of molecules having velocities along the X-axis is

Moderate

A

$\large nmv_x^2$
B

$nm\overline v _x^2$
C

$nmv_x^2$
D

none of these

Solution

${\overline v ^2}\, = \,\overline v _x^2 + \overline v _y^2 + \overline v _z^2\, = \,3\overline v _x^2\,$
$\overline v$ = RMS speed = $\sqrt {\frac{{3{p_x}}}{\rho }}$
$\rho$ = Density = nm
$\therefore \,{\overline v ^2}\, = \,\frac{{3{p_x}}}{\rho }\, \Rightarrow \,3\overline v _x^2\, = \,\frac{{3{p_x}}}{{nm}}$
$\Rightarrow \,{P_x}\, = \,nm\overline v _x^2$

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