Kinetic Theory of Gases
OBJECTIVE-I
(d) any of the three is possible.
(d) none of these.
OBJECTIVE-I
1. Which of the following parameters is the same for molecules of all gases at a given temperature?
(a) mass
(b) speed
(c) momentum
(d) kinetic energy
Answer: (d)
Explanation: The absolute temperature of a given sample of a gas is proportional to the total translational kinetic energy of its molecules.
Mass, speed, and momentum of a gas do not depend on the temperature.
2. A gas behaves more closely as an ideal gas at
(a) low pressure and low temperature
(b) low pressure and high temperature
(c) high pressure and low temperature
(d) high pressure and high temperature
Answer: (b)
Explanation: A gas behaves more closely as an ideal gas if its density is very low. It can be achieved if the pressure is low and the temperature is high.
3. The pressure of an ideal gas is written as p = 2E/3V. Here E refers to
(a) translational kinetic energy
(b) rotational kinetic energy
(c) vibrational kinetic energy
(d) total kinetic energy.
Answer: (a)
Explanation: If U = Total translational kinetic energy of all the molecules then, U = (3/2)nRT
→nRT = 2U/3
Now the ideal gas equation is
pV = nRT = 2U/3
→p = 2U/3V
Since in the problem the pressure is written as p = 2E/3V, hence E = U. So E refers to total translational kinetic energy of all the molecules.
4. The energy of a given sample of an ideal gas depends only on its
(a) volume
(b) pressure
(c) density
(d) temperature
Answer: (d)
Explanation: The absolute temperature of a given sample of a gas is proportional to the total translational kinetic energy of its molecules. So the energy of a given sample of a gas depends only on the temperature not on the pressure, volume or density.
5. Which of the following gases has maximum rms speed at a given temperature?
(a) hydrogen
(b) nitrogen
(c) oxygen
(d) carbon dioxide
Answer: (a)
Explanation: Since the kinetic energy of a gas U =(3/2)nRT.
So U depends only on T. For a given temperature the average kinetic energy of a molecule is the same. The kinetic energy depends upon the product of mass and the square of the speed. So a lighter molecule will have the maximum speed. Out of the given option hydrogen is the lightest hence has the highest rms speed.
6. Figure 24-Q1 shows graphs of pressure vs density for an ideal gas at two temperatures T₁ and T₂.
(a) T₁ > T₂
(b) T₁ = T₂
(c) T₁ < T₂
(d) any of the three is possible.
The figure for Q-6
Answer: (a)
Explanation: The ideal gas equation can also be written as
p=ρRT
So for a given ρ, p is higher for higher T. In the given figure, for ρ=A, p is more in T₁.
Hence T₁ > T₂.
7. The mean square speed of the molecules of a gas at absolute temperature T is proportional to
(a) 1/T
(b) √T
(c) T
(d) T².
Answer: (c)
Explanation: vᵣₘₛ² = 3kT/m =(3k/m)T
→vᵣₘₛ² ∝ T
8. Suppose a container is evacuated to leave just one molecule of a gas in it. Let vₐ and vᵣₘₛ represent the average speed and the rms speed of the gas.
(a) vₐ > vᵣₘₛ
(b) vₐ < vᵣₘₛ
(c) vₐ = vᵣₘₛ
(d) vᵣₘₛ is undefined.
Answer: (c)
Explanation: Since there is only one molecule, the speed will be constant, say v. The average speed, vₐ will be this constant speed. vₐ = v.
rms speed, vᵣₘₛ =√(Σv²/N) =√v² =v
(Since N=1)
Hence, vₐ = vᵣₘₛ.
9. The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about
(a) 125 m/s
(b) 2000 m/s
(c) 8000 m/s
(d) 31 m/s.
Answer: (b)
Explanation: Molecular weight of Oxygen = 32 g/mole, and that of hydrogen = 2 g/mole. Let m₁, m₂ be the masses and v₁, v₂ be the rms speeds of a oxygen and a hydrogen molecule respectively. Then m₁ = 16m₂.
At the same temperature, kinetic energy will be the same. So,
½m₁v₁² = ½m₂v₂²
→v₂² = (m₁/m₂)v₁²
→v₂ = √(m₁/m₂)*v₁
=√(16)*500 m/s
=2000 m/s.
10. The pressure of a gas kept in an isothermal container is 200 kPa. If half the gas is removed from it, the pressure will be
(a) 100 kPa
(b) 200 kPa
(c) 400 kPa
(d) 800 kPa.
Answer: (a)
Explanation: Since pV = nRT, here V and T are constant. R is the universal gas constant. So, p ∝ n. Since half the gas is removed, n becomes n/2. Hence p will now become p/2, i.e. 200/2 kPa =100 kPa.
11. The rms speed of oxygen molecules in a gas is v. If the temperature is double and the oxygen molecules dissociate into oxygen atoms, the rms speed will become
(a) v
(b) v√2
(c) 2v
(d) 4v.
Answer: (c)
Explanation: vᵣₘₛ = √(3kT/m) =v
Here temperature T' = 2T, and after dissociation of oxygen molecules, m' = m/2. Putting in the above equation,
v'ᵣₘₛ = √{3k*2T/(m/2)} =2√(3kT/m) =2v.
12. The quantity pV/kT represents
(a) mass of the gas
(b) the kinetic energy of the gas
(c) number of moles of the gas
(d) the number of molecules in the gas.
Answer: (d)
Explanation: The ideal gas equation can also be written as pV = NkT because of R=Nₐk and N=nNₐ. From this relation, N = pV/kT. So it represents the number of molecules in the gas.
13. The process on an ideal gas, shown in figure (24-Q2), is
(a) isothermal
(b) isobaric
(c) isochoric
(d) none of these.
The figure for Q-13
Answer: (c)
Explanation: The figure shows that p is directly proportional to T. So from the equation, pV=nRT
→p=(nR/V) T
V should also be constant. The constant volume process is isochoric.
14. There is some liquid in a closed bottle. The amount of liquid is continuously decreasing. The vapor in the remaining part
(a) must be saturated
(b) must be unsaturated
(c) maybe saturated
(d) there will be no vapor.
Answer: (b)
Explanation: In a liquid-vapor combination, the molecules from liquid go into vapor, also the molecules from vapor go into the liquid. When the vapor is unsaturated, the number of molecules going from liquid to vapor is more than coming back. So the amount of liquid decreases. Since the amount of the liquid is continuously decreasing here, the vapor is unsaturated.
15. There is some liquid in a closed bottle. The amount of liquid remains constant as time passes. The vapor in the remaining part
(a) must be saturated
(b) must be unsaturated
(c) maybe saturated
(d) there will be no vapor.
Answer: (a)
Explanation: Since the amount of liquid remains constant, the number of molecules going out and coming in is the same. It is because the remaining part can not hold more molecules so it must be saturated.
16. Vapor is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel
(a) increases continuously
(b) decreases continuously
(c) first increases and then decreases
(d) first increases and then becomes constant.
Answer: (d)
Explanation: The pressure will first increase because of the number of molecules increases in the constant volume. When the pressure equals the saturated vapor pressure, injected vapor will not remain as vapor but condense and the vapor pressure will be constant. Hence the option (d).
17. A vessel A has volume V and a vessel B has volume 2V. Both contain some water which hs a constant volume. The pressure in the space above water is pₐ for vessel A and pᵦ for vessel B.
(a) pₐ = pᵦ
(b) pₐ =2pᵦ
(c) pᵦ = 2pₐ
(d) pᵦ = 4pₐ
Answer: (a)
Explanation: Since the volume of water in both the vessels is constant, the vapor above the liquid in both the vessels is saturated. Hence both vapors are at saturated vapor pressure. So the option (a).
------------------------------------------------
Click here for all links → kktutor.blogspot.com
===<<<O>>>===
===<<<O>>>===
My Channel on YouTube → SimplePhysics with KK
Links to the Chapters
Links to the Chapters
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 8 - Work and Energy
Click here for → Question for Short Answers
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → Exercises (1-10)
Click here for → Question for Short Answers
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → Exercises (1-10)
Click here for → Exercises (11-20)
Click here for → Exercises (21-30)
Click here for → Exercises (31-42)
Click here for → Exercise(43-54)
Click here for → Exercises (21-30)
Click here for → Exercises (31-42)
Click here for → Exercise(43-54)
CHAPTER- 7 - Circular Motion
Click here for → Questions for Short Answer
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → EXERCISES (11-20)
Click here for → EXERCISES (21-30)
CHAPTER- 6 - Friction
Click here for → Questions for Short Answer
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → EXERCISES (11-20)
Click here for → EXERCISES (21-30)
CHAPTER- 6 - Friction
Click here for → Questions for Short Answer
Click here for → Questions for Short Answer
Click here for → OBJECTIVE-I
Click here for → Friction - OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → Exercises (11-20)
Click here for → EXERCISES (21-31)
Click here for → OBJECTIVE-I
Click here for → Friction - OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → Exercises (11-20)
Click here for → EXERCISES (21-31)
---------------------------------------------------------------------------------
---------------------------------------------------------------------------------
CHAPTER- 5 - Newton's Laws of Motion
Click here for → QUESTIONS FOR SHORT ANSWER
Click here for → QUESTIONS FOR SHORT ANSWER
Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
CHAPTER- 4 - The Forces
The Forces-
"Questions for short Answers"
Click here for "The Forces" - OBJECTIVE-I
Click here for "The Forces" - OBJECTIVE-II
Click here for "The Forces" - Exercises
--------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
CHAPTER- 3 - Kinematics - Rest and Motion
Click here for "Questions for short Answers"
Click here for "OBJECTIVE-I"
Click here for EXERCISES (Question number 1 to 10)
Click here for EXERCISES (Question number 11 to 20)
Click here for EXERCISES (Question number 21 to 30)
Click here for EXERCISES (Question number 31 to 40)
Click here for EXERCISES (Question number 41 to 52)
CHAPTER- 2 - "Physics and Mathematics"
CHAPTER- 2 - "Physics and Mathematics"
No comments:
Post a Comment