Physics Multiple Choice Questions on “Kinetic Theory of an Ideal Gas”.
1. Consider a gas enclosed in a box. A molecule of mass m, having a velocity -2i+3j+4k collides with a wall parallel to the xz plane. What will be its velocity after collision and its change in momentum? i,j & k are unit vectors along the x,y & z axis.
a) -2i-3j+4k, -6mj
b) 2i+3j-4k, -6mj
c) -2i-3j+4k, 6mj
d) 2i+3j-4k, 6mj
Answer: a
Clarification: On collision with a wall parallel to the xz plane, only the y-component will change.
Thus, new velocity will be -2i-3j+4k.
The change in momentum will be -3mj-3mj = -6mj.
2. Consider a gas enclosed in a box. Let the walls have an area of 0.01m2. 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
Answer: b
Clarification: 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
= nmAv2
= 10*10-20*0.01*4
= 4*10-21N.
3. Consider a gas inside a box. It exerts some pressure on its walls. Find this value. GIven that number of molecules per unit volume be 20, mass of each molecule 10-20kg, vx2 = 1m2/s2.
a) 20*10-20Pa
b) 20/3*10-20Pa
c) 20/3*10-19Pa
d) 20*10-19Pa
Answer: a
Clarification: Pressure is given by (1/3)nmv2.
v2 = 3vx2 = 3m2/s2.
P = (1/3)*20*10-20*3
= 20*10-20Pa.
4. Which of the following is not an assumption of KTG?
a) Time spent during collision is negligibly small
b) All gases are made up of molecules moving randomly in all directions
c) Molecules do not collide with each other
d) Molecules collide elastically with the wall
Answer: c
Clarification: According to KTG, molecules collide elastically with each other and with the walls of the container. The other given assumptions are true. These assumptions help to develop a model of molecular behavior of an ideal gas.
5. The number of molecules per unit volume in the sample is 20. The mass of each molecule is 10-20kg. The mean of speed squared is 4m2/s2. What is the value of internal energy of the gas? Assume volume of container is 0.02m3.
a) 0.8*10-20J
b) 0.53*10-20J
c) 0.01*10-20J
d) 0.45*10-20J
Answer: a
Clarification: Internal energy is given by: E = (1/2)Nmv2,
where N is the total number of molecules = nV.
E = 0.5*20*0.02*10-20*4
= 0.8*10-20J.
6. Average kinetic energy of a gas depends on which of the following factors?
a) Nature of gas
b) Temperature
c) Pressure
d) Volume
Answer: b
Clarification: Average kinetic energy is given by (3/2)kBT, which shows that it only depends on temperature.
7. A container has 3 gases whose mass ratio is 1:3:5. What is the ratio of mean square speed of the molecules of two gases? Their atomic masses are 20u, 30u & 40u corresponding to the order in which the ratios are given.
a) 2:3:4
b) 4:3:2
c) 2:√3:√2
d) √2:√3:2
Answer: b
Clarification: Their average kinetic energies will be the same. Thus, 1/2mv2will be the same.
v12:v22:v32 =m3:m2:m1
= 40:30:20
= 4:3:2.
8. What is the number of molecules in 3 cubic metre of a gas at 3atm & 27°C?
a) 2.17*10-20
b) 6.38*10-20
c) 3.86*10-20
d) 4.58*10-20
Answer: a
Clarification: Using, PV=NkT we get: N = PV/kT
= (3*3*105)/(1.38*10-23*300)
= 2.17*10-20.
9. Boyle’s law can be deduced from kinetic theory. True or False?
a) True
b) False
Answer: a
Clarification: From the kinetic theory we get: PV=(1/3)mNvrms2. Vrms2 depends only on temperature. So, if temperature is constant PV will be constant, which is Boyle’s law.