All exercise S.Qs of Chapter#06: Statistical Mechanics of Quantum Mechanics-II. We have arranged all S.Qs for BS/MSc Physics students.
Q.1 Why does a diatomic gas have greater energy content per mole than a monatomic gas at the same temperature?
Answer: We know that energy content is proportional to the number of degrees of freedom and as a diatomic gas has more degree of freedom, those of vibration and rotation than a monatomic gas, so diatomic gas has greater energy content per mole than a monatomic gas at the same temperature.
Q.2 A vessel is filled with gas at some equilibrium pressure and temperature. Can all gas molecules in the vessel have the same speed?
Answer: Speeds of gas molecules are governed by Maxwell-Boltzmann distribution law, so it is possible that all gas molecules in the vessel have the same speed under given conditions.
Q.3 Although the average speed of gas molecules in thermal equilibrium at some temperature is greater than zero, the average velocity is zero. Why?
Answer: If the average velocity is non-zero, then more molecules of gas would be moving in the direction of the average velocity. In a closed pot, this motion would result in a pressure difference within the tank that could not be sustained.
Q.4 Brownian motion cannot be observed with particles of large size. Explain.
Answer: Brownian motion is due to the bombardment of dispersed particles by molecules of medium which are themselves, in a state of continuous random motion. When particles are sufficiently large, the forces due to molecular collision almost completely balance. This is why Brownian motion cannot be observed with particles of large size.
Q.5 How Brownian motion can be increased in a gas?
Answer: Brownian motion increases due to increase in temperature of medium.
Q.6 If root square speed of atoms of an ideal gas is to be doubled, by what factor must the temperature of gas be increased?
Answer: Root mean square speed is given by the relation,
$$V_{rms}=\sqrt{\frac{3RT}{m}}\ \ \Rightarrow T=\frac{V_{rms}^2M}{3R}$$
Replacing $V_{rms}$ by $2V_{rms}$, we get
i.e., temperature increases four times.
Q.7 Why does smoke rise, rather than fall from a light candle?
Answer: As density of smoke from a light candle is smaller than density of ordinary air, so it rises instead of falling.
Q.8 Usually boiling point of water is 100oC When water is boiled at the top of mountain, is its temperature equal to 0oC ?
Answer: The boiling point of water is less than 100oC at the top of mountain since air pressure is less than it is at sea level.
Q.9 A gas is compressed at a constant temperature. What happens to the mean free path of the molecules in this process?
Answer: When gas is compressed at constant temperature, density of the gas increases and so the mean free path decreases.
Q.10 A vessel containing a fixed volume of a gas is cooled. Does the mean free path of the molecules increases, decreases, or remains constant in the cooling process?
Answer: For fixed volume, the density of the cooled gas cannot change, so the mean free path remains constant.
Q.11 If hot air rises, it is cooler at top of mountain than near the sea level. Why?
Answer: According to Joule Thomson effect when a compressed gas is allowed to a region of low pressure, it gets cooled. At top of the mountain pressure is low, so air (mixture of gasses) is cooler at top of the mountains than near the sea level.
Q.12 Real gas always cools when making a free expansion where as an ideal gas does not, why?
Answer: The molecules of real gas have definite size and intermolecular forces where as molecules of ideal gas point particles. Hence, real gases cool on expansion where as ideal gas does not.
Q.13 Explain why temperature decreases with the height in lower atmosphere.
Answer: The boiling point of a liquid deepens on pressure, with height, pressure decreases, so boiling point of the liquid decreases, and hence temperature decreases with height in lower atmosphere.
Q.14 Can ice be heated to a temperature above 0o without melting?
Answer: Ice cannot be heated to a temperature above 0oC because it changes to liquid on heating above C.
Q.15 Although real gases can be liquefied, but ideal gases cannot. Why?
Answer: The molecules of a real gas have a definite size and there are intermolecular forces in real gases, so on expansion real gas can be liquefied. The molecules of ideal gas are point particles and cannot be compressed as there is no space between molecules and hence question of liquefaction does not arise.
Q.16 The average speed of air molecules in a room is of the order of sped of sound. What is their average velocity?
Answer: Since the molecules move randomly in all directions, so average velocity of air molecules is zero in a room.
Q.17 Both water at 100oC and steam at 100oC causes serious burns. Is a burn produces by steam is same as a burn produced by water?
Answer: No, steam bum is most severe.
