Question

According to the kinetic theory of gases, the pressure exerted by a gas on the walls is measured as:
A. Rate of change of momentum imparted to the walls per second per unit area
B. Momentum imparted to the wall per unit area
C. Change of momentum imparted to the walls per unit area
D. Change in momentum per unit volume

Answer 1

Hint: The Newton’s second law of motion states that the force is the rate of change of momentum with respect to time.
$\Rightarrow F=\dfrac{dm}{dt}$

Complete step-by-step answer:
The kinetic theory of gases is based on the following concepts:
i. The particles of gas are moving in constant random motion
ii. The particle of gas strikes another particle of the gas and the vessel in which the gas is present. The collisions observed in the gas particle are completely elastic.
iii. The particles of the gas are very small, these particles occupy very small space in the whole volume of gas.
iv. The average kinetic energy of the gas is directly dependent on the temperature in Kelvin.

The pressure is defined as the ratio of the force and the area of application. It is also given as:
$\Rightarrow P=\dfrac{F}{A}$ … (1)
Where, F is the force and the A is the area

Using Newton’s second law of motion the force is given as:
$\Rightarrow F=\dfrac{dm}{dt}$ … (2)

Where, m is the momentum and t is the time

So, using equation (1) and (2):
The pressure of the gas is measured as the rate of the change of the momentum.

So, the correct answer is “Option A”.

Note: Another method:
The pressure of the gas is directly proportional to the force, when the area of application of force is constant.

$\Rightarrow P\propto F$ … (3)
But the force is directly proportional to the momentum of the particles.

$\Rightarrow F\propto m$ … (4)

So, using equation (3) and (4):
$\Rightarrow P\propto m$