61. What do you understand by internal energy of a gas?

According to the first law of thermodynamics, the total amount of heat supplied to the gas is utilized to increase its temperature and rest to do the work against the external pressure. The increase in the temperature of a gas is due to it has to do the work against the intermolecular force of attraction between gas molecules to expand, when heated. Hence, the total energy required to increase the temperature of a gas i.e. the energy required to do the work against the intermolecular force of attraction between gas molecules is termed as the internal energy of a gas.

 

62. Why has a gas two values of specific heat capacity?

When the gas is compressed suddenly when no heat is supplied (i.e. dQ=0) from outside then the temperature of the gas increases due to compression & its specific heat is zero as

                              

A gas will have infinite specific heat if and only if the gas is heated in such a way that its temperature is always constant (i.e. dt=0) but dQ is not equal to zero. The specific heat capacity of a gas is given as:

                          

As the specific heat of the gas can have any value oscillating in between zero to infinity depending on the matter in which the gas is being heated. But practically for easy consideration, there are two specific heat of a gas & they are:

1. Specific heat capacity at constant volume.

2. Specific heat capacity at constant pressure.

 

63. What happens to the internal energy of a gas during (a) isothermal expansion (b) adiabatic expansion?

During isothermal expansion, there is no change in the temperature so the internal energy of the gas remains unaltered i.e. dU = 0.

During adiabatic expansion, the work is done by gas at the expenses of its internal energy. So, during adiabatic expansion the internal energy of a gas falls (dU = -PdV).

 

64. Show that the efficiency of a heat engine is always less than 100%.

The efficiency of the heat energy is given by the relation:

                   

where, T₁ & T₂ are the temperature of the source and sink. For a heat engine to be perfectly efficient, the factor must be equal to zero. That means either T₂ must be zero or T₁ must be infinite. Hence, it is impossible that the temperature of the sink to be at absolute zero and also it is impossible that the temperature of the source is infinite. Hence, the efficiency of the heat engine is always less than 100%.

 

65. "Heat cannot be converted completely into mechanical work". Is this statement true? Explain.

"Heat cannot be converted completely into mechanical work". This statement is absolutely correct. The heat energy possessed by a body is the energy of the random motions of the molecules. The kinetic energy of a moving body represents the ordered motion which its molecules have superimposed on their random motion. When we convert heat energy into work then we are trying to change the random molecular motion into ordered motion. The thermal motions of molecules are random, it is impossible to convert all random motions into an orderly motion. So, heat cannot be converted completely into mechanical work.

 

66. Is the energy of a gas molecules zero at absolute zero of temperature? Explain.

No, the energy of a gas molecules is not zero at absolute zero of temperature. As the total energy of a gas is the sum of its potential energy & kinetic energy. Here, the kinetic energy of gas directly depends upon temperature but the potential energy is not. At higher temperatures, there is a great dependency of potential energy with temperature, but it is not the proportional one, as in case of kinetic. At absolute zero of temperature, the kinetic energy of a gas is zero but some potential energy still remains. So, the net energy of the gas is equal to the potential energy of the gas. Hence, at absolute zero of temperature, the energy of a gas molecules is not zero.

 

67. The oceans have tremendous amount of heat energy. Can't we utilize that heat energy for doing mechanical work? Justify your answer.

As the heat engine must possess source (at higher temperature) and sink (at lower temperature) in order to do the mechanical work by the engine. In order to perform mechanical work in ocean, there must be flow of heat from a source to sink according to the second law of thermodynamics. As the oceans have tremendous amount of heat energy i.e. source but there is no sink where the source can reject some heat energy to perform mechanical work. As the sink is absent, no mechanical work is done. Hence, the heat energy can not be utilized for doing mechanical work.

 

68. Why does the atmospheric air become cold when it rises up?

At higher altitudes of atmosphere, the air pressure is less (The atmosphere can be considered to be a sea of air, where upper atmosphere can be considered to be of less depth and lower atmosphere near the surface of earth can be considered to deep down.). Then according to the relation P = ρgh (h being the height of air available above it), the pressure at higher altitudes would be less. Since temperature of a gas system depends on the pressure, less pressure means less temperature. So when the atmospheric air rises up, they are exposed to lesser pressure, the temperature would gradually decrease.

 

69. What is the reason for difference in temperature of air coming out of a balloon due to its sudden bursting and the atmospheric air at the same place?

Yes, a gas always works when it expands in volume. The work done W by the gas is given by the relation:   dW = PdV

where, P is the pressure of the gas and dV is the change in volume.

 

70. Air pressure in cycle tyres increase during riding. Explain why?

The air pressure P inside the tyres is given by the relation:

                                     

where, ρ is the density of air molecules and c_av is the root mean square velocity of air molecules. Hence, the air pressure in cycle tyres is directly proportional to the square of the root mean square velocity of air molecules. As the air molecules inside the tyres are in vigorous motion during riding, its root mean square velocity also increases. Hence, the air pressure in cycle tyres increases during riding.    

 

71. A half filled water bottle is shaken vigorously. Does its temperature change? Explain

A half filled water bottle if shaken vigorously then the mechanical energy supplied is converted into heat energy (W = JQ) according to the conservation of energy. So, the mechanical work done against the intermolecular force of attraction between water molecules result in the increment of temperature of water. As a result, the temperature of the water inside the bottle rises. So, the there is change of temperature.

 

72. The "efficiency of all engines are less than that of the Carnot engine." Why?

As the carnot engine is considered as an ideal engine (that cannot be realized in practice) due to the fact that it is a reversible engine. In the carnot engine, there should be no loss of heat & no friction. Hence, its efficiency is always greater than other heat engines as there is loss of heat in other heat engines i.e. heat rejected to the sink and some energy is being lost as heat due to friction. Hence, an ideal concepts always dominates over practical concepts. Hence, the efficiency of all engines are less than that of the carnot engine.

 

73. "A carnot engine is called an ideal engine". Why?

A carnot engine is called an ideal engine because it cannot be realized in practice as well as due to the fact that it is a reversible engine. In the carnot engine, there should be no loss of energies. All the process in a carnot engine is slow. Hence, a carnot engine is called an ideal engine.

 

74. Refrigerator transfers heat from a cold body to a hot body. Does this violate the second law of thermodynamics?

Second law of thermodynamics states that:

1. No heat engine that works in a cycle completely converts heat energy into work.

2. When a cold body and a hot body are brought in contact with one another then heat always flows from the hot body to cold body. Or, It is impossible to construct a heat engine where the heat flows from colder body to hotter body without doing work in the working substance.

As the refrigerator is a heat engine that extracts heat from a cold body and transfers it to a hot body. This implies that a refrigerator is a heat engine that works reverse as other heat engine does. But it doesn't violets the second law of thermodynamics (which tell us that heat cannot by itself flow from a colder body to a hotter body) as the refrigerator transfers heat from a colder body to a hotter body by doing the work in the working substance. So, the principle of refrigerator doesn't violet the second law of thermodynamics.

 

75. Why will a refrigerator with a fixed amount of food consume more energy in a warm room than in a cold room?

A refrigerator is a heat engine that extracts heat from a cold body and transfers it to a hot body by doing the work in the working substance. Higher the difference in temperature between cold & hot body, more work is required to be done by the refrigerator. In warm room, temperature difference is high but in cold room, temperature difference is low. So, more work is to be done by the refrigerator in a warm room than in a cold room. Hence, a refrigerator with a fixed amount of food consume more energy in a warm room than in a cold room.