Question

Number of collisions per unit time of molecules of a gas on the wall of a container per $m^2$ will increase if

• A. Temperature and volume both are doubled
• B. Temperature and volume both are halved
• C. Pressure and temperature both are doubled
• D. Pressure and temperature both are halved

Answer 1

Answer: (B), (C)

Pressure and temperature both are doubled
Temperature and volume both are halved

Number of collisions per unit time $\propto \frac{1}{\text{time between two collision}\times area}$
$\to \frac{\dot{n}}{A}\propto \frac{V_{rms}}{\text{distance b/w walls}\times A}{V}_{rms}\propto \sqrt{T}$
distance b/w walls \times A $=$ volume
So , $\frac{\dot{n}}{A}\propto \frac{T^{1/2}}{V}$
$\frac{\dot{n}}{A}\propto \frac{P}{T^{1/2}}$
If both T and V are halved,or T and P are doubled , $\frac{\dot{n}}{A}$ increases.