water to steam. The steam is then directed at the blades of a turbine, setting it rotating. Finally, the mechanical energy associated with this rotation is used to drive an electric generator. In another heat engine - the internal combustion engine in an automobile - energy enters the engine as fuel is injected into the cylinder and combusted, and a fraction of this energy is converted to mechanical energy.
In general, a heat engine carries some working substance through a cyclic process during which (1) energy is transferred by heat from a source at a high temperature, (2) work is done by the engine, and (3) energy is expelled by the engine by heat to a source at lower temperature. As an example, consider the operation of a steam engine in which the working substance is water. The water in the engine is carried through a cycle in which it first evaporates into steam in a boiler and then expands against a piston. After the steam is condensed with cooling water, it returns to the boiler, and the process is repeated.
The thermal efficiency of a heat engine is defined as the work done by the engine, divided by the energy absorbed during one cycle. We can think of thermal efficiency as the ratio of the benefit received (work) to the cost incurred. Heat engines can operate in reverse. The work is done in the compressor unit of the refrigerator, compressing a refrigerant such as freon, causing its temperature to increase. A household air conditioner is another example of a heat pump. Some homes are both heated and cooled by heat pumps.
There are limits to the efficiency of heat engines. The ideal engine would convert all input energy into useful work, but it turns out that such an engine is impossible to construct. The Kelvin-Planck formulation of the second law of thermodynamics can be stated as follows: No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely for the performance of an equal amount of work.
To summarize, the first law says we can't get a greater amount of energy out of a cyclic process than we put in, and the second law says we can't break even. No engine can operate with 100% efficiency, but different designs yield different efficiencies, and it turns out one design in particular delivers the maximum possible efficiency. This design is the Carnot cycle. Understanding it requires the concepts of reversible and irreversible processes. In a reversible process, every state along the path is an equilibrium state, so the system can return to its initial conditions
66
by going along the same path in the reverse direction. A process that doesn't satisfy this requirement is irreversible.
The Laws of Thermodynamics
Thermodynamic |
Work |
|
|
processes |
done on |
|
|
|
the sys- |
|
|
|
tem |
|
|
First law of |
Isolated |
Surroundings |
Jiggling |
thermodynamics |
system |
Molar specific |
|
|
|
heat |
|
|
|
Isobaric pro- |
|
|
|
cess |
|
|
|
Adiabatic |
|
|
|
process |
|
|
|
Isovolumetric |
|
|
|
process |
|
|
|
Isothermal |
|
|
|
processes |
|
Second law of |
Heat en- |
Cyclic pro- |
Internal combus- |
thermodynamics |
gine |
cess |
tion engine |
|
|
|
Power plant |
|
|
|
Movable piston |
|
|
Thermal effi- |
Reversible pro- |
|
|
ciency |
cesses |
|
|
|
Irreversible pro- |
|
|
|
cesses |
|
|
|
Refrigerators |
|
|
|
Heat pumps |
|
|
Carnot cycle |
Carnot engine |
|
Entropy |
Disorder |
Boltzman’s con- |
|
|
|
stant |
Third law of |
Friction |
Brevity of cy- |
Maximum effi- |
thermodynamics |
|
cles |
ciency |
Fig. 12. Thesaurus for Unit 12
67
The Carnot Engine
In 1824, in an effort to understand the efficiency of real engines, a French engineer named Sadi Carnot (1796-1832) described a theoretical engine now called a Carnot engine that is of great importance from both a practical and a theoretical viewpoint. He showed that a heat engine operating in an ideal, reversible cycle-now called a Carnot cycle - between two energy reservoirs is the most efficient engine possible. Such an engine establishes an upper limit on the efficiencies of all real engines. Carnot's theorem can be stated as follows: No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.
According to the third law of thermodynamics, it's impossible to lower the temperature of a system to absolute zero in a finite number of steps, so such reservoirs are not available, and the maximum efficiency is always less than one. In most practical cases, the cold reservoir is near room temperature, about 300 K, so increasing the efficiency requires raising the temperature of the hot reservoir. All real engines operate irreversibly, due to friction and the brevity of their cycles, and are therefore less efficient than the Carnot engine.
A state variable called the entropy is related to the second law of thermodynamics. We define entropy on a macroscopic scale as the German physicist Rudolf Clausius (1822-1888) first expressed it in 1865. The concept of entropy gained wide acceptance in part because it provided another variable to describe the state of a system, along with pressure, volume, and temperature. Its significance was enhanced when it was found that the entropy of the Universe increases in all natural processes. This is yet another way of stating the second law of thermodynamics.
Entropy originally found its place in thermodynamics, but its importance grew tremendously as the field of statistical mechanics developed. One of the main conclusions of the statistical mechanical approach is that isolated systems tend toward greater disorder, and entropy is a measure of that disorder.
1.What laws of thermodynamics do you know?
2.How many ways of transferring energy between a system and its surroundings do you know?
3.Name four types of thermal processes.
4.Give the Kelvin-Planck formulation of the second law of thermodynamics.
68
5.Why law is the concept of entropy connected with?
6.What is the principle of work of Carnot engine?
Exercises
1. Rearrange the letters in the anagrams to form equivalents for the Russian words:
Окружающая среда |
Surdingsround |
|
|
Холодильник |
friregerator |
Двигатель |
gineen |
|
|
Энтропия |
troepyn |
Неупорядоченность |
sorderdi |
|
|
2. Match the words in A with the words in B to form word combinations:
A |
B |
Movable |
pumps |
Thermodynamic |
piston |
Isovolumetric |
engine |
Heat |
process |
Carnot |
plant |
Power |
variable |
3. Fill in the gaps with the missing words from the list:
internal energy, adiabatic process, entropy, thermodynamic variables, degree of freedom
1.The _____ of any isolated system must remain constant.
2.When a system isn't isolated, the change in internal energy will be zero if the system goes through a cyclic process in which all the
_____ - pressure, volume, temperature, and moles of gas - return to their original values.
3.Each different way a gas molecule can store energy is called a
_____.
4.A sufficiently rapid process may be considered approximately
_____ because there isn't time for any significant transfer of energy by heat.
5.The concept of _____ is satisfying because it enables us to present the second law of thermodynamics in the form of a mathematical statement.
69
P A R T III
Vibrations and Waves
UNIT 13
VIBRATION AND WAVES
Read the following texts. Study the thesaurus on fig. 13, answer the questions after the texts
Periodic motion, from masses on springs to vibrations of atoms, is one of the most important kinds of physical behavior. In this Unit we take a more detailed look at Hooke's law, where the force is proportional to the displacement, tending to restore objects to some equilibrium position. A large number of physical systems can be successfully modeled with this simple idea, including the vibrations of strings, the swinging of a pendulum, and the propagation of waves of all kinds. All these physical phenomena involve periodic motion.
Periodic vibrations can cause disturbances that move through a medium in the form of waves. Many kinds of waves occur in nature, such as sound waves, water waves, seismic waves, and electromagnetic waves. These very different physical phenomena are described by common terms and concepts introduced here.
Hooke's law
One of the simplest types of vibrational motion is that of an object attached to a spring, previously discussed in the context of energy in Unit 5. We assume that the object moves on a frictionless horizontal surface. If the spring is stretched or compressed a small distance x from its unstretched or equilibrium position and then released, it exerts a force on the object. The value of the spring constant k is a measure of the stiffness of the spring. Stiff springs have large k values, and soft springs have small the spring constant values. A restoring force always pushes or pulls the object toward the equilibrium position.
Simple harmonic motion occurs when the net force along the direction of motion obeys Hooke's law - when the net force is proportional to the displacement from the equilibrium point and is always directed toward the equilibrium point. Not all periodic motions over the same path can be classified as simple harmonic motion. A ball being tossed back
70