Question

If 10²² gas molecules each of mass 10^-26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m² with a speed 10⁴ m/s, the pressure exerted by the gas molecules will be of the order of:
1. 10⁴ N/m²
2. 10⁸ N/m²
3. 10³ N/m²
4. 10¹⁶ N/m²

Answer 1

Correct Answer - Option 1 : 10⁴ N/m²

Concept:

Kinetic theory of gases explains the behaviour of gases which consists of the moving atoms or molecules rapidly in random motion.

In a container, the gas molecules collide against the wall continuously. While colliding, the momentum is transferred to the walls of the container. The pressure exerted by gas is determined by the continuous collision where the walls of the container experiences the force equal to the total momentum.

Calculation:

Given, Mass of the particle, m = 10^-26 kg

Velocity of the particle, V = 10⁴ m/s

Number of particles, N = 10²²

Area on which pressure is excreted, A = 1 m²

The pressure exerted by the gas molecules is given by the formula:

\({\rm{P}} = \frac{{\left( {2{\rm{mV}}} \right){\rm{N}}}}{{\rm{A}}}\) 

\(\Rightarrow {\rm{P}} = \frac{{2 \times {{10}^{ - 26}} \times {{10}^4} \times {{10}^{22}}}}{1}\) 

∴ P = 2 N/m²