Thermal Physics. Topics to be covered. Slide 2 / 105. Slide 1 / 105. Slide 3 / 105. Slide 4 / 105. Slide 5 / 105. Slide 6 / 105.

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1 Slide 1 / 105 Slide 2 / 105 Topics to be covered Thermal Physics Temperature and Thermal quilibrium Gas Laws Internal nergy Heat Work Laws of Thermodynamics Heat ngines Slide 3 / 105 Thermodynamics System Originally, in 1824 Sadi arnot describe a thermodynamics system as the working substance under study. In Thermodynamics - system is any region completely enclosed within a well defined boundary. verything outside the system is then defined as surroundings. Very often in this chapter we will use a word "system" instead of cylinder of gas, container filled with water, ice cube. Slide 4 / 105 Temperature The concept of temperature is rooted in qualitative ideas of "hot" and "cold" based on our sense of touch. n object that feels hot has a higher temperature than a similar object that feels cold. Measuring temperature based on our sense is very subjective. When we touch different objects in our classroom we will find that metallic objects feel cooler than wooden or plastic objects which is not true because they have all been in the same room for a long time. They all have the same temperature. Slide 5 / 105 Temperature Slide 6 / 105 Temperature Thermometers are instruments designed to measure temperature. There is a better way of measuring temperature based on properties of matter that depend on temperature. The volume of liquid, length of a metal rod, gas pressure, electroconductivity, and the color of a hot glowing object.

2 Slide 7 / 105 Temperature In everyday life, we use liquid-in-tube thermometers which are based on thermal expansion of liquids. In addition to thermometers we need some kind of a common scale that we can use to present different temperatures. Slide 8 / 105 Temperature The relationships among three different temperature scale are presented by the table below. In urope, the most common is elsius scale. In the United State, the most common is Fahrenheit scale. In science, the most important is bsolute or Kelvin scale. Slide 9 / 105 Temperature The following formulas we can use to convert temperature from one scale to another. Slide 10 / Which temperature scale never gives negative temperatures? Fahrenheit Kelvin elsius Reaumur ll of the above Slide 11 / 105 Slide 12 / Freezing point of water is 32 F; what is this on elsius scale? Room temperature is often taken to be 68 F; what is this on the elsius scale?

3 Slide 13 / 105 Slide 14 / The temperature of a human body is 37 ; what is this on the Fahrenheit scale? The temperature of boiling water is 100 ; what is this on the Fahrenheit scale? Slide 15 / 105 Slide 16 / Melting point of ice is 0 ; what is this on the Kelvin scale? bsolute zero is what temperature on the elsius scale? Slide 17 / 105 Thermal quilibrium and the Zeroth Law of Thermodynamics Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium. The zeroth law of thermodynamics says that if two objects are each in equilibrium with a third object, they are also in thermal equilibrium with each other. Slide 18 / Three objects,, and initially have different temperatures T >T >T. Objects and are separated by an insulating plate but they are in contact with object through a conducting platform. Which of the following is true when objects and reach thermal equilibrium with object? The temperature of all three objects stays unchanged Object has higher temperature than object and Object has higher temperature that object and Object has higher temperature that object and ll three objects have the same temperature

4 Slide 19 / 105 Slide 20 / simple pendulum is made of a steel string supporting a brass sphere. The temprerature in a room with the pendulum is increased from 15 to 30. Which of the folowing is true about the period of oscillations? The period is doubled The period stays unchanged The period is increased by #2 The period is decreased by #2 The period is slightly increased Slide 21 / 105 Thermal xpansion Volume thermal expansion occurs when increasing temperature causes increases in volume for both solid and liquid materials. Where # is the coefficient of volume expansion. Slide 22 / glass flask is filled with glycerin up to the top. When the temperature of surroundings is increased by a few degrees, which of the following is true about the level of glycerin in the flask? (The coefficients of volume expansion are:# glycerin=49x10-5 K -1, # glass= 2x10-5 K -1 ) The level of glycerin in the flask goes down The level of glycerin stays unchanged because the both expand Glycerin spills out of the flask It can't be determined from the given information Slide 23 / 105 Thermal xpansion Water, in the temperature range from 0 o to 4 o, decreases in its volume and increases in density. bove 4 o, water expands when heated. Hence water has its greatest density at 4 o. Water also expands when it freezes, which is why a piece of ice floats on water surface. Slide 24 / 105 Many properties of matter such as: thermal expansion, melting, boiling, cooling, heating... can be explained based on the concept that matter is made up of tiny particles.

5 Slide 25 / 105 The idea that all familiar matter is made up of atoms goes back to the ancient Greeks. ccording to them if we were cut a piece of iron into smaller and smaller portions, eventually a smallest piece of iron would be obtained which could not be divided further. This smallest piece is called an atom (indivisible). Slide 26 / 105 studies the macroscopic properties of matter in terms of its atomic structure and behavior. This theory has a tremendous practical importance; once we have this understanding, we can design materials with specific desired properties. The analysis to this theory has led to development of highstrength steels, glasses with special optical properties, semiconductors. Slide 27 / 105 The study of a real gas is very complicated from mathematical point of view. In our discussion of the kinetic theory we will be using a simplified mathematical model which is called - ideal gas. Slide 28 / 105 The assumptions of ideal gas model are: 1. container contains a very large number of particles (atoms, molecules). 2. The atoms behave as point particles; their size is small in comparison to the average distance between particles and to the size of the container. 3. The particles are in constant motion; they obey Newton's Laws of motion. ach particle collides occasionally with a wall of the container. These collisions are perfectly elastic. 4. The walls of the container are rigid and very massive. Slide 29 / Which of the following is not included into the assumptions of the ideal gas? The number of molecules in a container is very large The molecules interact when they collide with each other The molecules interact all the time during their motion because of intermolecular forces The collisions between molecules are perfectly elastic The size of molecules can be ignored Slide 30 / 105 Now we will calculate the pressure in the ideal gas based on kinetic theory. First we will find the change in momentum during one single collision of a molecule with a wall of the container. The change in momentum in the direction perpendicular to the wall is: ssuming that the collision is perfectly elastic and

6 Slide 31 / 105 If a molecule is going to collide with a given wall area during a small time interval #t, which is the time it takes the molecule to travel across the box and back again, a distance equal to 2L. Where 2L = v x #t. Slide 32 / 105 The time between the collisions is very small, so the number of collisions per second is very large. ccording to Newton's Laws the average force will be equal to the force exerted during one collision divided by the time between the collisions. Slide 33 / 105 To calculate the force due to all the molecules in the box, we have to add the contributions of each. The average value of the square of the x component of velocity is Slide 34 / 105 The force due to all molecules is From Pythegorian Theorem: Since all molecules move in random directions and there is no preference between x, y, and z we can write the following: or Slide 35 / 105 Now we can change the square of the velocity component to the square of the velocity. Slide 36 / 105 The last equation can be modified by replacing average velocity with the average kinetic energy of molecules. The pressure on the wall is force per unit of area. or It was found from the series of experiments that which is called the ideal-gas equation. Where k= 1.38x10-23 J/K is oltzmann's constant.

7 Slide 37 / 105 fter comparing two last equations we can conclude: The average kinetic energy of molecules in a gas is directly proportional to the absolute temperature. This is the most important result of kinetic theory. The higher the temperature, the faster molecules move on the average. Slide 38 / 105 When we analyze two equations: and We can find the root-mean-square velocity or v rms Slide 39 / 105 Summary to the : 1. The pressure in the ideal gas is directly proportional to the average square of the velocity of molecules. The faster the molecules move the more frequent they collide with the walls and greater change in the momentum during the collisions. Slide 40 / 105 Summary to the : 2. The first time in the history of physics the temperature was explained on the microscopic level not based on human sense. ccording to the kinetic theory, the temperature can't be negative and it reaches zero (absolute zero) when the average translational kinetic energy of molecules is zero. Slide 41 / 105 Summary to the : 3. The average velocity of molecules depends on absolute temperature and molecular mass. The increasing temperature causes molecules to move faster and light molecules move faster then heavy ones. Slide 42 / If the average kinetic energy of molecules is increased while the number of moles is kept constant, what happens to the pressure of an ideal gas? It increases It decreased It remains constant It decreases and then increases None from the above

8 Slide 43 / 105 Slide 44 / The average kinetic energy of molecules can be increased by increasing which of the following? 14 If the temperature of an ideal gas is increased from 25 to 50, what happens to the average kinetic energy of the molecules? Pressure It doubles Volume It quadruples Temperature It is cut to one-half Number of moles It is cut to one-fourth ll of the above It slightly increases Slide 45 / 105 Slide 46 / If the absolute temperature of an ideal gas is doubled, what happens to the average speed of the molecules? It doubles It quadrupes It increases by #2 It decreases by #2 It remains unchanged, like other theories in physics, requires an experimental proof. Historically, the experiments with gasses were performed long time before the completion of the kinetic theory. In the next section of the chapter, we will discuss the Gas Laws that were discovered by different scientists. Slide 47 / 105 Gas Laws oyle's Law-the pressure in a gas is inversely proportional to its volume when the temperature is kept constant. This process is called "Isothermal". Slide 48 / Which of the following graphs represents the isothermal process? constant

9 Slide 49 / container with an ideal gas at pressure P is compressed to onefourth of its volume while the temperature is kept constant. What is the new pressure in the gas in terms of P? 2P 4P P 1/2P 1/4P Slide 50 / 105 Gas Laws harles's Law- the volume of a given amount of gas is directly proportional to the absolute temperature when the pressure is kept constant. This process is called "Isobaric". Slide 51 / 105 Slide 52 / Which of the following graphs represents the isobaric process? 19 n ideal gas is taken from one state at the temperature T 1=273 K to another state at the temperature T 2 =546 K isobarically. What happens to the volume of the ideal gas? It quadruples It is cut to one-fourth It doubles It is cut to a half It doesn't change during the isobaric process Slide 53 / 105 Gas Laws Gay-Lussac's Law- the pressure of a gas is directly proportional to the absolute temperature, when the volume stays unchanged. This process is called "Isochoric". Slide 54 / Which of the following graphs represents the isochoric process?

10 Slide 55 / sample of an ideal gas is enclosed into a container with rigid walls. The temperature of the gas is changed from 20 o to 60 o. What happens to the pressure in the gas? It doubles It quadruples It triples It is cut to one-third It is slightly increased Slide 56 / 105 Gas Laws Gas Laws can be combined into a single more general relationship between the pressure, volume, and temperature a fixed quantity of gas. Where n is the number of moles and R is the universal gas constant. This equation is called the Ideal Gas Law. Slide 57 / 105 Slide 58 / The number of moles of an ideal gas is doubled while the temperature and volume remain the same. What happens to the pressure in the gas? 23 n ideal gas is taken through a closed cycle. s shown on the diagram. Which point is associated with the highest temperature? It doubles It quadruples It remains the same It is decreased to one-half ll points are related to the same temperature It is decreased to one-fourth More information is required Slide 59 / 105 Slide 60 / 105 Internal nergy Similar to mechanics when we use two different approaches - dynamics and energy to explain the same processes, can be done in thermal physics. In the previous section, we spend time to explain thermal processes by using three parameters: pressure, volume, and temperature. In the following section we will be using more elegant - energy approach to explain the same thermal processes. Internal nergy When a pendulum is set to oscillations over a long period of time we can observe that its amplitude decreases to zero. It seems like mechanical energy disappeared, which is not true because the temperature of the pendulum and surroundings has changed. The mechanical energy is transformed into the kinetic energy of molecules.

11 Slide 61 / 105 Slide 62 / 105 Internal nergy The internal energy of an ideal gas depends on temperature and the number of moles of gas. n increase in temperature causes an increase in internal energy. Slide 63 / 105 Slide 64 / The temperature of a monatomic ideal gas is increased from 35 o to 70 o. How does it change its internal energy? It doubles It quadruples It is slightly increased It is decreased to one-half It is decreased to one-fourth 25 The state of an ideal gas is changed through the closed path What happens to the internal energy of the gas between point 2 and point 3? It increases It decreases It remains constant It decreases and then increases It increases and then decreases Slide 65 / 105 Internal nergy The state of any thermodynamic system can be described with the internal energy. The internal energy of a thermodynamic system can be changed in two different ways: adding heat to the system or doing work on the system. Slide 66 / 105 Heat We introduced the concept of internal energy now it is time to explain the concept of heat. Heat is a transfer of energy from one object to another because of difference in temperature. Where m - mass, #T - change in temperature, and c - specific heat. Specific heat is a quantity characteristic of the material.

12 Slide 67 / 105 Slide 68 / The mechanical equivalent of heat was measured by Kelvin oltzmann oyle Joule harles 27 The amount of heat required to raise the temperature of 1 kg of a substance by 1 o is referred to which of the following? Latent heat of vaporization Latent heat of fusion Specific heat alorie Joule Slide 69 / The ocean temperature doesn't change drastically because of Water is a good heat conductor Wather is a good heat radiator Water has a very high specific heat Water has a very low melting temperature Water has a very high boiling point Slide 70 / 105 Heat When a system changes its phase from solid to liquid a certain amount of energy is involved. L F is the heat of fusion. The energy required to change a substance from the liquid to the vapor can be presented by the following formula. L V is the heat of vaporization. Slide 71 / 105 Slide 72 / When a solid metal melts its temperature 30 Which of the following is true about melting process? Increases ecreases Remains constant Increases and then decreases ecreases and then increases The energy is required to increase the average kinetic energy of molecules The energy is required to decrease the average kinetic energy of molecules The energy is required to increase the potential energy between the molecules The energy is required to decrease the potential energy between the molecules No energy is required for this process it happens spontaneously

13 Slide 73 / When water vapor condenses The temperature increases The temperature decreases The energy is absorbed The energy is released None from the above Slide 74 / 105 Heat Heat can be transfered from one object to another in three different ways: conduction, convection, and radiation. onduction is a transfer of heat as a result of molecular collisions. Slide 75 / 105 onduction onduction is a transfer of heat as a result of molecular collisions. is the rate of heat transfer. k- constant, is called the thermal conductivity, which is characteristic of the material. Slide 76 / When we double the thickness of a wall with the same material, the rate of heat loss due to the same temperature difference across the thickness is oubled Quadrupled Unchanged ut to one-half ut to one-fourth Slide 77 / 105 onvection onvection is the process where heat is transfered by the mass movement of molecules from one place to anoter. Slide 78 / onvection can occur Only in solids Only in liquids Only in gasses Only in liquids and gasses In solids, liquids, and gasses onvection in gasses onvection in liquids

14 Slide 79 / Which of the following is responsible for raising the temperature of water in a pot placed on a hot stove? onduction onvection Radiation Vaporization ondensation Slide 80 / 105 Radiation nergy transfer by electromagnetic waves. Stefan-oltzmann equation. The rate at which an object radiates energy is proportional to the fourth power of the absolute temperature. e - emissivity, is a number between 0 and 1 that depends on the material. Slide 81 / When the temperature of a heater is doubled, by what factor does the radiating power change? Slide 82 / 105 Work in Thermodynamics simple and very common example of a thermodaymic system is a quantity of gas enclosed in a cylinder with a movable piston Slide 83 / 105 Work in Thermodynamics First we consider the work done by the gas during its expansion. n expanding gas always dose positive work. Suppose that the cylinder has a cross-sectional area and the pressure exerted by the gas is P gas. The total force exerted by the gas on the piston is F = p. When the piston moves up a distance #x and the pressure P is constant, the work W is Slide 84 / 105 Work in Thermodynamics When the piston moves down, so the volume of the gas decreases, then the work done by the gas is negative. uring the compression of the gas in the cylinder the work done by the external force F ext is positive. The relationship between work done by the gas and work done on the gas can be presented by following:

15 Slide 85 / 105 Work in Thermodynamics This relationship can be represented as a graph of p as a function of V on a pv - diagram. The work done equals the area under the curve on a pv-diagram. In an expansion, the work done by the gas is positive. Slide 86 / 105 Work in Thermodynamics In a compression, the work done by the gas is negative. Slide 87 / 105 Slide 88 / The state of an ideal gas is changed in a closed path Which of the following is true about work done by the gas between point 1 and point 2? 37 The state of an ideal gas is changed in a closed path Which of the following is true about work done by the gas between point 2 and point 3? Work done by the gas is positive Work done by the gas is positive Work done by the gas is negative Work done by the gas is negative Work done by the gas is zero Work done by the gas is zero Work done by the gas is greater than work done on the gas Work done by the gas is greater than work done on the gas Work done by the gas is less than work done on the gas Work done by the gas is less than work done on the gas Slide 89 / 105 Slide 90 / 105 First Law of Thermodynamics First Law of Thermodynamics In previous sections of this chapter we defined the internal energy, heat, and work in thermodynamics. Now we will combine them in one formulaconservation of energy in thermal processes. First Law of Thermodynamics where Q is the net heat added to the system, W' is the net work done on the system, and #U is the change in internal energy.

16 Slide 91 / 105 Slide 92 / J of heat is added to a system and 100 J of work done on the system. What is the change in the internal energy of the system? 250 J 150 J 100 J 50 J 0 J J of heat is added to a system and the system does 100 J of work on surroundings. What is the change in the internal energy of the system? 250 J 150 J 100 J 50 J 0 J Slide 93 / 105 First Law of Thermodynamics Isothermal process is one where temperature stays unchanged. When T = constant #T = 0. The internal energy of an ideal gas depends on temperature and for this process #U = 0 Since the change in internal energy is zero the First Law of Thermodynamics: The heat added to the gas in an isothermal process equals the work done by the gas. Slide 94 / 105 First Law of Thermodynamics diabatic process is one in which no heat flows into or out of the system. When heat is zero then the first law of thermodynamics: The net work done on the gas equals the change in internal energy. Slide 95 / 105 First Law of Thermodynamics Isochoric process is one where volume stays unchanged. When #V = 0 W' = 0 The first law of thermodynamics is The net heat added to the system equals the change is internal energy. Slide 96 / sample of an ideal gas is taken through a closed cycle. Which of the following is true about the change in internal energy and work done on the gas between point 2 and point 3? #U =0, W' > 0 #U =0, W' = 0 #U =0, W' < 0 #U > 0, W' > 0 #U < 0, W' < 0

17 Slide 97 / 105 Second Law of Thermodynamics Many thermal processes proceed naturally in one direction but not the opposite. For example, heat by itself always flows from a hot object to a cooler object, never the reverse. The reverse process would not violate the first law of thermodynamics; energy would be conserved. Slide 98 / 105 Second Law of Thermodynamics Heat flows naturally from a hot object to a cold object; heat never flows spontaneously from a cold object to a hot object. In order to fix this problem with reversible processes, scientists formulated a new principle-the second law of thermodynamics. Slide 99 / 105 Heat ngines The basic idea behind of any heat engine is that mechanical energy can be obtained from thermal energy. enis Papin first time in history of physics described three basics components of any heat engine: high-temperature reservoir, low-temperature reservoir, and engine containing gas or steem. Slide 100 / 105 Heat ngines The high-temperature reservoir transfers an amount of heat Q H to the engine, where part of it is transformed into work W (during the expansion of gas) and the rest, Q L, is exhausted to the lowtemperature reservoir. Slide 101 / 105 Heat ngines The efficiency e of any heat engine can be defined as a ratio of work W to the heat input Q H. Slide 102 / 105 Heat ngines The question of increasing the efficiency of a heat engine was very difficult in physics. This question was answered in 1824 by the French engineer Sadi arnot. Sadi arnot developed a hypotetical, idealized heat engine that has the maximum possible efficiency consistent with the second law of thermodynamics.

18 Slide 103 / 105 Heat ngines The arnot engine consists of two reversible isothermal processes,, and two reversible adiabatic processes,. The arnot engine operates between two temperature T H and T L. Slide 104 / 105 Heat ngines arnot Theorem- no engine can have more efficiency than a arnot engine operating between the same two temperatures. arnot ideal efficiency Slide 105 / 105 Second Law of Thermodynamics and ntropy The total entropy of an isolated system never decreases (Second Law of Thermodynamics). The change in entropy S of a system, when heat Q is added to it by a reversible process at a constant temperature T. ntropy is a measure of the disorder of a system. For any real process, the change in entropy is greater than zero:# S>0.