Question

Consider a gas enclosed in a box. Let the walls have an area of 0.01m^2. Let’s say a few molecules having their x-component of velocity =2m/s, hit a wall parallel to the yz plane. What will be the value of force on the wall in time dt? Let the number of molecules per unit volume be 10 & mass of each molecule be 10^-20kg.

(a) 4*10^-19N

(b) 4*10^-21N

(c) 4/3*10^-21N

(d) 4/3*10^-19N

The question was asked by my school principal while I was bunking the class.

Enquiry is from Kinetic Theory of an Ideal Gas topic in portion Kinetic Theory of Physics – Class 11

Answer 1

Right option is (b) 4*10^-21N

Best explanation: According to the assumptions of KTG, we will assume that the molecules collide elastically.

 The total momentum transferred to the wall is 2mv*(1/2)nAvdt.

1/2 has been included because, on average, half the molecules near that wall will be moving away from the wall.

Force will be momentum/time

= nmAv^2

= 10*10^-20*0.01*4

= 4*10^-21N.