0 Thermal Physics 2009

AN INTRODUCTION TO THERMAL PHYSICS The particle theory (kinetic theory of matter) The particulate theory of matter postulates that: • Matter is made out of extremely small particles • Particles move constantly in empty space. Even in solids, these particles are moving although they do not change places but vibrate around fixed positions. • The higher the temperature, the faster they move until at the melting point they are free to move and slide past each other. Anyhow at any temperature some particles can escape from the others and turn into vapour or gas. This “pressure” towards vaporisation increases until at the boiling point all particles are energetic enough to “get rid” of the rest. The distances between particles in the gaseous state are about a tenfold greater than the average particle size. The arrangements of particles in solids, liquids and gases A simple view of the arrangement of the particles in solids, liquids and gases looks like this:

Solids In the solid, the particles are touching, and the only motion allowed to them is vibration. The particles may be arranged regularly (in which case, the solid is crystalline), or at random (giving waxy solids like candles or some forms of polythene, for example). The particles are held in the solid by forces which depend on the actual substance. Melting and freezing If energy is supplied by heating the solid, the heat energy causes greater vibrations until the particles eventually loosen from each other to form a liquid. When a liquid freezes, the reverse happens. At some temperature, the motion of the particles is slow enough for the forces of attraction to be able to hold the particles as a solid. As the new bonds are formed, heat energy is evolved. Liquids In a liquid, the particles are mainly touching, but some gaps have appeared in the structure. These gaps allow the particles to move, and so the particles are arranged randomly. The forces that held the solid particles together are also present in the liquid, but in a somewhat loosened form.

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Boiling and condensing If more heat energy is supplied, the particles eventually move fast enough to break all the attractions between them, and the liquid boils. If the gas is cooled, at some temperature the gas particles will slow down enough for the attractions to become effective enough to condense it back into a liquid. Again, as those forces are reestablished, heat energy is released. Gases In a gas, the particles are entirely free to move. At ordinary pressures, the distance between individual particles is of the order of ten times the diameter of the particles. At that distance, any attractions between the particles are fairly negligible. Internal Energy Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects. For example, a room temperature glass of water sitting on a table has no apparent energy, either potential or kinetic. But on the microscopic scale it is a seething mass of high speed particles travelling at hundreds of meters per second. If the water were tossed across the room, this microscopic energy would not necessarily be changed when we superimpose an ordered large scale motion on the water as a whole.

U is the most common symbol used for internal energy. Microscopic Energy Internal energy involves energy on the microscopic scale. For an ideal monoatomic gas, this is just the translational kinetic energy of the linear motion of the "hard sphere" type atom and the behaviour of the system is well described by kinetic theory. However, for polyatomic gases there is rotational and vibrational kinetic energy as well. Then in liquids and solids there is potential energy associated with the intermolecular attractive forces. A simplified visualization of the contributions to internal energy can be helpful in understanding phase transitions and other phenomena which involve internal energy.

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Heat Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess "heat"; the appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object this is properly called heating. Mechanical Equivalent of Heat Heat flow and work are both ways of transferring energy. In a classic experiment in 1843, James Joule showed the energy equivalence of heating and doing work by using the change in potential energy of falling masses to stir an insulated container of water with paddles. Careful measurements showed the increase in the temperature of the water to be proportional to the mechanical energy used to stir the water. At that time calories were the accepted unit of heat and joules became the accepted unit of mechanical energy. Their relationship is 1 calorie = 4,1868 joule First Law of Thermodynamics The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes:

The first law makes use of the key concepts of internal energy, heat, and system work. It is used extensively in the discussion of heat engines. In the context of chemical

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reactions and process, it may be more common to deal with situations where work is done on the system rather than by it. Temperature A convenient operational definition of temperature is that it is a measure of the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules. The flow of heat is from a high temperature region toward a lower temperature region. The details of the relationship to molecular motion will not be further discussed in this course. The temperature defined from kinetic theory is called the kinetic temperature. Temperature is not directly proportional to internal energy since temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy. Temperatures are measured in one of the three standard temperature scales (Celsius, Kelvin, and Fahrenheit). Temperature Scales The Celsius, Kelvin, and Fahrenheit temperature scales are shown in relation to the phase change temperatures of water. The Kelvin scale is called absolute temperature and the Kelvin is the SI unit for temperature. In case the absolute zero could be reached (the third principle of Thermodynamics forbids this) the particles of the system would have no kinetic energy at all!

The freezing point of water at one atmosphere pressure, 0.00°C, is 0.01K below that at 273.15 K. If you want to be really precise about it, the boiling point is 373.125 K, or 99.75 °C. But for general purposes, just 0 °C and 100 °C are precise enough. Thermal Equilibrium It is observed that a higher temperature object which is in contact with a lower temperature object will transfer heat to the lower temperature object. The objects will approach the same temperature, and in the absence of loss to other objects, they will then maintain a constant temperature. They are then said to be in thermal equilibrium. Thermal equilibrium is the subject of the Zeroth Law of Thermodynamics.

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Zeroth Law of Thermodynamics The "zeroth law" states that if two systems are at the same time in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

If A and C are in thermal equilibrium with B, then A is in thermal equilibrium with B. Practically this means that all three are at the same temperature, and it forms the basis for comparison of temperatures. It is so named because it logically precedes the other two. Second Law of Thermodynamics The second law of thermodynamics is a general principle which places constraints upon the direction of heat transfer and the attainable efficiencies of heat engines. In so doing, it goes beyond the limitations imposed by the first law of thermodynamics. Its implications may be visualized in terms of the waterfall analogy.

Second Law: Heat Engines Second Law of Thermodynamics: It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir. This precludes a perfect heat engine. This is sometimes called the "first form" of the second law, and is referred to as the Kelvin-Planck statement of the second law. Second Law: Refrigerator Second Law of Thermodynamics: It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature

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object. This precludes a perfect refrigerator. The statements about refrigerators apply to air conditioners and heat pumps, which embody the same principles. This is the "second form" or Clausius statement of the second law.

Second Law: Entropy Second Law of Thermodynamics can be stated this way: In any cyclic process the entropy will either increase or remain the same. Now what is entropy? Entropy:

A state variable whose change is defined for a reversible process at T where Q is the heat absorbed.

Entropy:

A measure of the amount of energy which is unavailable to do work.

Entropy: A measure of the disorder of a system.

Since entropy gives information about the evolution of an isolated system with time, it is said to give us the direction of "time's arrow". If snapshots of a system at two different times show one state which is more disordered, then it could be implied that this state came later in time. For an isolated system, the natural course of events takes the system to a more disordered (higher entropy) state. Heat Conduction Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If one end of a metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end 6

because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones. Heat conductivity is different for different substances. Metals are very good heat conductors but rubber, wood or plastic are not. Heat Convection Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it. Convection above a hot surface occurs because hot air expands, becomes less dense, and rises. Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy.

Convection can also lead to circulation in a liquid, as in the heating of a pot of water over a flame. Heated water expands and becomes more buoyant. Cooler, denser water near the surface descends and patterns of circulation can be formed, though they will not be as regular as suggested in the drawing.

In ordinary heat transfer on the Earth, it is difficult to quantify the effects of convection since it inherently depends upon small nonuniformities in an otherwise fairly homogeneous medium. In modelling things like the cooling of the human body, we usually just lump it in with conduction.

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Heat Radiation Radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the emitting object. Radiation travels through empty space and that is the mechanism through which our planet receives energy from the Sun. As any object emits electromagnetic radiation because of their movement of its particles (according to the electromagnetic theory of Maxwell’s) all objects will radiate unless it s particles are at rest that is at absolute zero. For ordinary temperatures (less than red hot), the radiation is in the infrared region of the electromagnetic spectrum. This region corresponds to the Infra Red zone of the spectrum As matt black is the colour that corresponds to the absorption of almost all radiation, black objects will absorb radiation more intensely when exposed. Surfaces painted black will rise their temperatures faster than if they were painted white or silver. But the best absorbers are the best emitters and because of this reason these matt black painted surfaces cool down more easily than the others. This fact is very important when it is necessary to promote or prevent heat interchanges with the environment.

PROBLEMS ON THERMAL PHYSICS 1- State the difference between temperature, internal energy and heat. In what units are they measured? Do we use the same instrument to measure heat and temperature? 2- Draw diagrams showing: (a) a gas changing into a liquid; (b) a solid changing into a gas; (c) a substance mixing spontaneously because of molecular motion through a liquid. Name the three processes. 3- Explain the term “absolute zero” in terms of molecular motion and express in Kelvin the following temperatures: 0°C; -154°C; 28°C, -273°C. 4- Two objects at 20°C and 300K respectively are put in close contact. (a) What happens with the internal energy of each object? What “moves” from one to the other? When does this “movement” stop? 5- Look for a solar panel used for heating water in a textbook and explain the following features: (a) The pipes are made out of copper and these and the rest of the inner part of the panel are painted matt black. (b) The panel is covered with a glass lid. (c) The panel box is made out of thick Styropor (Telgopor). 6- (a) Many freezers at the supermarkets have no lids. Give a reason for this not being anti-economical. What would happen in case they had a lid? (Not a sliding lid but a hinged one). (b) The temperature shown by a thermometer placed under the sun is not the same as the surrounding air’s temperature. Explain this fact. (c) Air is a very good insulator but it is used so, just if it is in small compartments (e.g. wool or Styropor pores); could you explain why this is so? (d) It is not possible to cool a room keeping an opened fridge inside; in fact, the temperature will rise inside the room if you do so! Explain both facts. 7- Explain why an evaporating liquid gets cooler. 8- Inside the Earth’s nucleus the radioactive decay of Uranium causes thermal energy to be generated. Name and explain the processes by which this energy could: (a) reach the mantle; (b) reach the lithosphere; (c) move through the atmosphere; (d) leave the planet. 9- Energy from the Sun is fundamental for life processes. Explain how this energy: 8

(a) reaches the Earth’s atmosphere (b) gets to the Earth’s surface. 10- Describe the greenhouse effect. Why is it now being enhanced? 11- You have learned during the course that an ice-cream radiates heat waves. Does it get then progressively colder? Why do we feel a cold sensation when we approach our hand to it? 12- State the first and second principles of Thermodynamics. 13- An inventor claims that he has built an engine that takes out heat energy from a tank containing 100 Kg of water at 100°C, and transfers it to another tank with the same amount of water at 20°C. The machine works until both tanks are at 50°C and 1000 KJ of mechanical work have been done. If 1Kg of water absorbs (or releases) 4.18 KJ for each 1°C temperature change: (a) Calculate the total energy given out by the hot water tank. (b) Calculate the energy absorbed by the cold one. (c) According to your calculations is the inventor a fake? 14- At a Patent Office some inventors apply for patents on different inventions. Which of them you will immediately reject? (a) An apparatus that uses electric energy and whose only effect is heating a room. (b) An apparatus that uses electric energy and whose only effect is cooling a room (c) A portable air conditioner that can be placed in the middle of a closed room. (d) An apparatus that defrosts food using heat taken out from the environment. (e) An apparatus that uses all the thermal energy of a flame to change it into useful work.

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