Laws of Thermodynamics
QUESTIONS FOR SHORT ANSWER
QUESTIONS FOR SHORT ANSWER
1. Should the internal energy of a system necessarily increase if heat is added to it?
Answer: The increase in the internal energy (ΔU) of a system is equal to the amount of heat given (ΔQ) minus the amount of work (ΔW) done by it.
ΔU = ΔQ - ΔW
If ΔW = ΔQ, the change in internal energy is zero. So the internal energy does not necessarily increase if heat is given to the system.
2. Should the internal energy of a system necessarily increase if its temperature is increased?
Answer: The internal energy of a system increases if the total kinetic energy of all the molecules increases and this thing increases with the increase in the temperature. Hence the internal energy of a system necessarily increases if its temperature is increased.
3. A cylinder containing gas is lifted from the first floor to the second floor. What is the amount of work done on the gas? What is the work done by the gas? Is the internal energy of the gas increased? Is the temperature of the gas increased?
Answer: Since there is no change in the volume of the gas, no work is done on the gas nor any work is done by the gas.
No, the internal energy of the gas is not increased because the systematic movement of a gas sample has no effect on temperature.
4. A force is applied on a block of mass M. The block is displaced through a distance d in the direction of the force. What is the work done by the force on the block? Does the internal energy change because of this work?
Answer: The work done by the force F here = F*d.
No, the internal energy of the block does not change. This work done is reflected either as a change of kinetic energy or potential energy.
5. The outer surface of a cylinder containing gas is rubbed vigorously by a polishing machine. The cylinder and its gas become warm. Is the energy transferred to the gas heat or work?
Answer: Since the volume of the gas does not change, the energy transferred is not due to work. The energy to the gas is transferred by the cylinder which is in the form of heat that is generated due to friction.
6. When we rub our hands they become warm. Have we applied heat to the hands?
Answer: No. It is the mechanical work done by us to overcome the force of friction between the hands which converts into heat energy.
7. A closed bottle contains some liquid. The bottle is shaken vigorously for 5 minutes. It is found that the temperature of the liquid is increased. Is heat transferred to the liquid? Is work done on the liquid? Neglect expansion on heating.
Answer: No, heat is not transferred to the liquid.
Work done is equal to the force times displacement. Assuming that the bottle is kept at the initial position after shaking, the displacement is zero. So no work is done on the liquid. But in the shaking of the liquid work is done against the viscous forces, also it increases the total kinetic energy of the molecules. So the internal energy of the liquid and temperature increases.
8. The final volume of the system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?
Answer: If the final volume of the system is equal to the initial volume, then the process is either isochoric or cyclic. The cyclic process may be either reversible or irreversible. In the isochoric process, the work done is zero. In the reversible process, the done by the system and the work done on the system is compensated and final work done is zero. In the irreversible process, the work done by the system is not equal to the work done on the system. Hence the final work done is not zero.
Thus the answer to both the questions is "no".
9. Can work be done by a system without changing its volume?
Answer: If the system is not changing its volume the process is called isochoric. In this process, work can not be done because ΔW = p*ΔV =p*0 =0.
10. An ideal gas is pumped into a rigid container having diathermic walls so that the temperature remains constant. In a certain time interval, the pressure in the container is doubled. Is the internal energy of the contents of the container also doubled in the interval?
Answer: n = pV/RT, here, V, R, and T are constant, so when pressure is 2p, the number of moles = 2n.
Since the mass or number of moles of the gas is doubled, the internal energy associated with the original mass is also doubled in the contents of the cylinder.
11. When a tire bursts, the air coming out is cooler than the surrounding air. Explain.
Answer: The tire burst is a sudden process in which heat transfer between the system and the surrounding can not take place. So it is an adiabatic process. The pressure of the air inside the tire is more than the surrounding. Due to the tire burst, the volume of the air increases and some work is done by the air for which it uses its internal energy. So the internal energy of the system decreases. It results in a decrease in the temperature of the expanded air and feels cooler than the surrounding.
12. When we heat an object, it expands. Is the work done by the object in this process? Is heat given to the object equal to the increase in its internal energy?
Answer: ΔW =p*ΔV
Not only gases, but it is also true for the expansion of solids and liquids.
In the given problem, p is constant but due to expansion ΔV has some positive value. Hence some work is done by the object.
Now the change in the internal energy,
ΔU = ΔQ - ΔW
Since ΔW is not zero, ΔU < ΔQ. So the heat given to the object is not equal to the increase in the internal energy.
13. When we stir a liquid vigorously, it becomes warm. Is it a reversible process?
Answer: When a liquid is vigorously stirred it becomes warm because the work is done against the viscosity. But the process is dissipative. A dissipative process can not be reversible. Another point is that if mechanical work is done on the system to increase the internal energy the reverse process is not automatic but we need a heat engine to do it that also only a part of the heat energy can be used to do the mechanical work. So it is not a reversible process.
14. What should be the condition for the efficiency of a Carnot engine to be equal to 1?
Answer: The efficiency of a Carnot engine, η = 1 - Q₂/Q₁, where Q₁ is the heat applied to the engine and Q₂ is the heat given to the sink. It is clear that η can be equal to 1 only when Q₂ is zero but it is not possible according to the second law of thermodynamics which is also called Kelvin-Planck statement.
15. When an object cools down, heat is withdrawn from it. Does the entropy of the object decrease in the process? If yes, is it a violation of the second law of thermodynamics stated in terms of an increase in entropy?
Answer: Yes, when the heat is withdrawn from an object its entropy decreases.
The second law of thermodynamics may be stated as "It is not possible to have a process in which the entropy of an isolated system is decreased". Here the cooling object is not an isolated system. The heat given out by the object is added to the surroundings and its entropy increases. The universe along with the object is taken as an isolated system. And its entropy is not decreasing. Hence the second law of thermodynamics is not violated.
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Links to the Chapters
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CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
EXERCISES - Q-11 to Q-18
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
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- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
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"
