Question

A container has an ideal gas at pressure $P$ . Assuming the mass of a molecule are moving with same speed $v$ in random directions. The expression for number of collisions per second which the molecules make with unit of area of container wall is :

• A. $\frac{P}{mv}$
• B. $\frac{3P}{2mv}$
• C. $\frac{\sqrt{3}P}{2mv}$
• D. $\frac{3P}{\sqrt{2}mv}$

Answer 1

Answer: (A)

$\frac{P}{mv}$

Consider the number of molecules having velocity $v$ that strike the wall area$A$in the time interval$dt$.

Then, the area of the imaginary cylinder will be$v.dt$.

If the number of the molecules pr unit volume is given as $\frac{N}{V}$

Total number of the molecules will be $\frac{N}{V}vdtA$

$\frac{dP}{dt}=F=m{v}^2\frac{N}{V}A$

$P=\frac{F}{A}=m{v}^2\frac{N}{V}$

Number of collision per second will be $\frac{P}{mv}$