Slide 36 / 105 Kinetic Theory The last equation can be modified by replacing average velocity with the average kinetic energy of molecules. It was found from the series of experiments that which is called the ideal-gas equation. Where k= 1.38x10 -23 J/K is Boltzmann's constant.
Slide 37 / 105 Kinetic Theory After 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 Kinetic Theory When we analyze two equations: and We can find the root-mean-square velocity or v rms
Slide 39 / 105 Kinetic Theory Summary to the Kinetic Theory: 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 Kinetic Theory Summary to the Kinetic Theory: 2. The first time in the history of physics the temperature was explained on the microscopic level not based on human sense. According 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 Kinetic Theory Summary to the Kinetic Theory: 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 / 105 12 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? A It increases B It decreased C It remains constant D It decreases and then increases E None from the above
Slide 43 / 105 13 The average kinetic energy of molecules can be increased by increasing which of the following? A Pressure B Volume C Temperature D Number of moles E All of the above
Slide 44 / 105 14 If the temperature of an ideal gas is increased from 25 C to 50 C, what happens to the average kinetic energy of the molecules? A It doubles B It quadruples C It is cut to one-half D It is cut to one-fourth E It slightly increases
Slide 45 / 105 15 If the absolute temperature of an ideal gas is doubled, what happens to the average speed of the molecules? A It doubles B It quadrupes It increases by # 2 C It decreases by # 2 D E It remains unchanged
Slide 46 / 105 Kinetic Theory Kinetic Theory, 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 Boyle's Law-the pressure in a gas is inversely proportional to its volume when the temperature is kept constant. This process is called "Isothermal". constant
Slide 48 / 105 16 Which of the following graphs represents the isothermal process? C B A D E
Slide 49 / 105 17 A container with an ideal gas at pressure P is compressed to one- fourth of its volume while the temperature is kept constant. What is the new pressure in the gas in terms of P? A 2P B 4P C P D 1/2P E 1/4P
Slide 50 / 105 Gas Laws Charles'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 18 Which of the following graphs represents the isobaric process? C B A D E
Slide 52 / 105 19 An 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? A It quadruples B It is cut to one-fourth C It doubles D It is cut to a half E 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 / 105 20 Which of the following graphs represents the isochoric process? C B A D E
Slide 55 / 105 21 A sample of an ideal gas is enclosed into a container with rigid walls. The temperature of the gas is changed from 20 o C to 60 o C. What happens to the pressure in the gas? A It doubles B It quadruples C It triples D It is cut to one-third E 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 22 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? A It doubles B It quadruples C It remains the same D It is decreased to one-half E It is decreased to one-fourth
Slide 58 / 105 23 An ideal gas is taken through a closed cycle A ⇒ B ⇒ C ⇒ A. As shown on the diagram. Which point is associated with the highest temperature? A A B B C C D All points are related to the same temperature E More information is required
Slide 59 / 105 Internal Energy 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.
Slide 60 / 105 Internal Energy 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.
Slide 61 / 105
Slide 62 / 105 Internal Energy The internal energy of an ideal gas depends on temperature and the number of moles of gas. An increase in temperature causes an increase in internal energy.
Slide 63 / 105 The temperature of a monatomic ideal gas is increased from 35 o C 24 to 70 o C. How does it change its internal energy? A It doubles B It quadruples C It is slightly increased D It is decreased to one-half E It is decreased to one-fourth
Slide 64 / 105 25 The state of an ideal gas is changed through the closed path 1 ⇒ 2 ⇒ 3 ⇒ 1. What happens to the internal energy of the gas between point 2 and point 3? A It increases B It decreases C It remains constant D It decreases and then increases E It increases and then decreases
Slide 65 / 105 Internal Energy 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.
Slide 67 / 105 26 The mechanical equivalent of heat was measured by A Kelvin B Boltzmann C Boyle D Joule E Charles
Slide 68 / 105 27 The amount of heat required to raise the temperature of 1 kg of a substance by 1 o C is referred to which of the following? A Latent heat of vaporization B Latent heat of fusion C Specific heat D Calorie E Joule
Slide 69 / 105 28 The ocean temperature doesn't change drastically because of A Water is a good heat conductor B Wather is a good heat radiator C Water has a very high specific heat D Water has a very low melting temperature E 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 29 When a solid metal melts its temperature A Increases B Decreases C Remains constant D Increases and then decreases E Decreases and then increases
Slide 72 / 105 30 Which of the following is true about melting process? The energy is required to increase the average kinetic energy of A molecules The energy is required to decrease the average kinetic energy of B molecules The energy is required to increase the potential energy between C the molecules The energy is required to decrease the potential energy between D the molecules E No energy is required for this process it happens spontaneously
Slide 73 / 105 31 When water vapor condenses A The temperature increases B The temperature decreases C The energy is absorbed D The energy is released E 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. Conduction is a transfer of heat as a result of molecular collisions.
Slide 75 / 105 Conduction Conduction 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 / 105 32 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 A Doubled B Quadrupled C Unchanged D Cut to one-half E Cut to one-fourth
Slide 77 / 105 Convection Convection is the process where heat is transfered by the mass movement of molecules from one place to anoter. Convection in Convection in liquids gasses
Slide 78 / 105 33 Convection can occur A Only in solids B Only in liquids C Only in gasses D Only in liquids and gasses E In solids, liquids, and gasses
Slide 79 / 105 34 Which of the following is responsible for raising the temperature of water in a pot placed on a hot stove? A Conduction B Convection C Radiation D Vaporization E Condensation
Slide 80 / 105 Radiation Energy transfer by electromagnetic waves. Stefan-Boltzmann 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 / 105 35 When the temperature of a heater is doubled, by what factor does the radiating power change? A 2 B 4 C 8 D 16 E 32
Slide 82 / 105 Work in Thermodynamics A 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. An expanding gas always dose positive work. Suppose that the cylinder has a cross-sectional area A and the pressure exerted by the gas is P gas . The total force exerted by the gas on the piston is F = pA. 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. During 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:
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 36 The state of an ideal gas is changed in a closed path 1 ⇒ 2 ⇒ 3 ⇒ 1. Which of the following is true about work done by the gas between point 1 and point 2? A Work done by the gas is positive B Work done by the gas is negative C Work done by the gas is zero D Work done by the gas is greater than work done on the gas E Work done by the gas is less than work done on the gas
Slide 88 / 105 37 The state of an ideal gas is changed in a closed path 1 ⇒ 2 ⇒ 3 ⇒ 1. Which of the following is true about work done by the gas between point 2 and point 3? A Work done by the gas is positive B Work done by the gas is negative C Work done by the gas is zero D Work done by the gas is greater than work done on the gas E Work done by the gas is less than work done on the gas
Slide 89 / 105 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 formula- conservation of energy in thermal processes.
Slide 90 / 105 First Law of Thermodynamics 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.
Slide 91 / 105 38 150 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? A 250 J B 150 J C 100 J D 50 J E 0 J
Slide 92 / 105 39 250 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? A 250 J B 150 J C 100 J D 50 J E 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 Adiabatic 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 / 105 40 A 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? A # U =0, W' > 0 # U =0, W' = 0 B # U =0, W' < 0 C D # U > 0, W' > 0 E # U < 0, W' < 0
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. In order to fix this problem with reversible processes, scientists formulated a new principle-the second law of thermodynamics.
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.
Slide 99 / 105 Heat Engines The basic idea behind of any heat engine is that mechanical energy can be obtained from thermal energy. Denis 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 Engines 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 low- temperature reservoir.
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