Kinetic Theory of Gases
OBJECTIVE-II
OBJECTIVE-II
1. Consider a collision between an oxygen molecule and a hydrogen molecule in a mixture of oxygen and hydrogen kept at room temperature. Which of the following are possible?
(a) The kinetic energies of both the molecules increase.
(b) The kinetic energies of both the molecules decrease.
(c) The kinetic energy of the oxygen molecule increases and that of the hydrogen molecule decreases.
(d) The kinetic energy of the hydrogen molecule increases and that of the oxygen molecule decreases.
Answer: (c), (d)
Explanation: Since the collision is fully elastic, kinetic energies of both the molecules can not increase or decrease simultaneously, because of the total momentum and energy will not be conserved (Kinetic energy increases or decreases if the speed increases or decreases).
Hence the option (c) and (d) depending upon the directions of velocity before the strike.
2. Consider a mixture of oxygen and hydrogen kept at room temperature. As compared to a hydrogen molecule an oxygen molecule hits the wall
(a) with a greater average speed
(b) with a smaller average speed
(c) with greater average kinetic energy
(d) with smaller average kinetic energy.
Answer: (b)
Explanation: The average kinetic energy of both the molecules will be the same because the temperature is the same. Since the oxygen molecule is heavier than hydrogen, it will have a smaller average speed for the same kinetic energy. Thus the option (b).
3. Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium?
(a) kinetic energy
(b) momentum
(c) density
(d) speed.
Answer: (b)
Explanation: Since the gas has mass and volume, the density can not be zero. Option (c) is wrong. The kinetic energy and the speed are scalers i.e. they have only magnitudes, hence they will be simply added and can not be zero. The momentum is a vector quantity and has the same direction that of the velocity. In the equilibrium condition, the gas has no net velocity hence the average momentum for the molecules is zero.
4. Keeping the number of moles, volume and temperature the same, which of the following are the same for all ideal gases?
(a) rms speed of a molecule
(b) density
(c) pressure
(d) average magnitude of momentum.
Answer: (c)
Explanation: The rms speed, density and the average magnitude of the momentum will depend upon the mass of the molecules of the ideal gas in consideration. But the pressure will remain the same because p=nRT/V and here all on the right side are constants.
5. The average momentum of a molecule in a sample of an ideal gas depends on
(a) temperature
(b) number of moles
(c) volume
(d) None of these.
Answer: (d)
Explanation: As discussed in Q-3, the average momentum of a molecule in an ideal gas sample is zero. Hence the option (d).
6. Which of the following quantities is the same for all ideal gases at the same temperature?
(a) the kinetic energy of 1 mole
(b) the kinetic energy of 1 g
(c) the number of molecules in 1 mole
(d) the number of molecules in 1 g.
Answer: (a), (c)
Explanation: The average kinetic energy of a molecule is the same for all gasses at a fixed temperature. Since 1 mole of any gas contains the same number of molecules, the kinetic energy of 1 mole of all the gases at the same temperature will have the same kinetic energy. Hence the option (a) and (c). One gram of different gases will have different numbers of molecules hence the option (b) and (d) not true.
7. Consider the quantity MkT/pV of an ideal gas where M is the mass of the gas. It depends on the
(a) the temperature of the gas
(b) the volume of the gas
(c) the pressure of the gas
(d) nature of the gas.
Answer: (d)
Explanation: MkT/pV = MkT/nRT
=Mk/nR = M*K,
(where K =k/nR = constant).
So the quantity in consideration does not depend on pressure, volume or temperature of the gas. It only depends on the mass of the gas M. But M = mN where m is the molecular weight and N is the number of molecules. The molecular weight depends on the nature of the gas. Hence the option (d).
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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
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CHAPTER- 7 - Circular Motion
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CHAPTER- 6 - Friction
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CHAPTER- 6 - Friction
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CHAPTER- 5 - Newton's Laws of Motion
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CHAPTER- 4 - The Forces
The Forces-
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CHAPTER- 3 - Kinematics - Rest and Motion
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CHAPTER- 2 - "Physics and Mathematics"
CHAPTER- 2 - "Physics and Mathematics"
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