Chapter 7: Heat, Temperature and Thermodynamics PDF Lecture Notes

Chapter 7: Heat, Temperature and Thermodynamics Physics 100 Lecture Note 1  Heat, temperature and thermodynamics Outline ▪ What is heat ( or thermal energy) ▪ What is the temperature ▪ What is pressure ▪ Thermal expansion of gases and solids ▪ First and second law o...

Chapter 7: Heat, Temperature and Thermodynamics Physics 100 Lecture Note 1  Heat, temperature and thermodynamics Outline ▪ What is heat ( or thermal energy) ▪ What is the temperature ▪ What is pressure ▪ Thermal expansion of gases and solids ▪ First and second law of thermodynamics ▪ Heat pumps, heat engine and entropy Physics 100 Lecture Note 2  Air and heat Air, wind and molecular motion ▪ Air is composed of different gases (mainly nitrogen and oxygen) ▪ These gases are composed of molecules (except helium, argon etc., which are a tiny percentage of the air) ▪ Average speed of gas molecules in the air is about 500 m/s (or 1800 km/h) ▪ In a normal day (i.e.,25 ̊ C, normal pressure) there are 2.69 × 1025 molecules in a volume of 1𝑚3 (2.69 × 1016 molecules in a volume of 1 𝑚𝑚3 ) ▪ The mean free-path of a gas molecule in the air (i.e., the distance a molecule travel before it bounces off another molecule) is 6.7 × 10−6 𝑐𝑚 ▪ Conclusion: Molecules have very high speed but the space they travel is filled with molecules so they are constantly bumping into each other Physics 100 Lecture Note 3  Motion of molecules in the air Molecule type % of air Average speed 𝑁2 78 450 m/s (1620 km/h) 𝑂2 21 420 m/s (1500 km/h) 𝐴𝑟 0.39 380 m/s (1370 km/h) 𝐶𝑂2 0.03 357 m/s (1290 km/h) Table: Composition and average of speed of air ▪ Average time between molecular collisions in the atmosphere is 2 × 10−9 ▪ This mean that on average a molecule will collide with other molecule 5 × 108 times in one second! Physics 100 Lecture Note 4  Molecular motion Three types of molecular motion Figure: Different ways molecules move Conclusion: Molecules move around, rotate, and vibrate at the same time Physics 100 Lecture Note 5  Energy and molecular motion Molecular motions 1 ▪ A moving molecule has speed and mass (remember KE = 2 𝑚𝑣 2 ) A molecule had kinetic energy ▪ While moving around, a molecule also rotates and rotation is a form of motion Because of the rotational motion, molecules have rotational energy ▪ Also while a molecule moves around and rotates at the same time, it also vibrates and the vibration is repetative form of motion Because of vibrational motion, a vibrating molecule has vibrational energy ▪ Your typical nitrogen or oxygen molecule in the air moves around, rotates and vibrates at the same that it frequently bounces off other molecules ▪ During collision, gas molecules exchange energy do their kinetic, rotational, and vibrated at the same that it frequently bounces off other molecules Physics 100 Lecture Note 6  Thermal energy of a gas Total energy of a gas molecule ▪ Any amount of air (i.e, of gas molecules) contains a huge number of frequently colliding molecules ▪ At any moment of time, each gas molecules has a certain amount of motion So molecule in the air has a certain amount of energy (in the form of kinetic, rotational, and vibration energy) ▪ If we could measure these energies (we can’t!), to find the total energy of molecules, we would add them up Total energy = kinetic energy + rotational energy + vibrational energy ▪ The total energy of a gas molecule at any time is the sum of its kinetic rotational and vibrational energy Physics 100 Lecture Note 7  Motion and energy in solids ▪ The only possible mode of motion in a solid is vibration ▪ In a solid, atoms can have small vibrational motion about their equilibrium position ▪ Thermal energy in a solid is a manifestation of these small motions ▪ Addition of heat to the solid increases these motion ▪ With a sufficient amount of heat, atoms in the solid acquire enough motion to overcome the forces holding them in place and the solid melts Physics 100 Lecture Note 8  Thermal energy of a gas … Thermal energy ▪ If we could measure these total energy of every molecules in certain amount of a gas (say in a container), then we would know the total energy such gas carries ▪ And we would call it amount of thermal energy or heat in gas ▪ The total energy of a gas composed of molecules is equal to the total energy of the molecules it is composed of Physics 100 Lecture Note 9  Average thermal energy and temperature Definition of temperature ▪ In the case of a solid, the average energy of the atoms in the solid is 𝑇𝑜𝑡𝑎𝑙 𝑉𝐸 Average energy =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 ▪ Remember KE,RE and VE stand for kinetic energy, rotational energy, and vibrational energy respectively. ▪ The temperature of thermal system (gas, liquid or solid), is defined as 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑒𝑛𝑟𝑔𝑦 Temperature = 𝐾 𝐵 10−23 𝐽 ▪ 𝐾𝐵 is called Boltzmann constant and it is equal to 1.38 × 𝐾 ▪ The temperature defined here is not usual scales (centigrade/fahrenheit) we use daily ▪ It is called the absolute or Kelvin (K) scale Physics 100 Lecture Note 10  Temperature Temperature A number that corresponds to the warmth or coldness of an object Measured by a thermometer Is a per-particle property Temperature is proportional to the average translational kinetic energy per particle in a substance. Gas—how fast the gas particles are bouncing to and from Liquid—how fast particles slide and jiggle past one another Solid—how fast particles move as they vibrate and jiggle in place Physics 100 Lecture Note 11  Thermometer Measures temperature by expansion or contraction of a liquid (mercury or colored alcohol). Reading occurs when the thermometer and the object reach thermal equilibrium (having the same average kinetic energy per particle). Temperature scale Celsius scale named after Anders Celsius (1701–1744). 0°C for freezing point of water to 100°C for boiling point of water. Fahrenheit scale named after G. D. Fahrenheit (1686–1736). 32°F for freezing point of water to 212°F for boiling point of water. Kelvin scale named after Lord Kelvin (1824–1907). 0 K for freezing point of water to 373 K for boiling point of water 0 at absolute zero; same size degrees as Celsius scale kelvins, rather than degrees, are used Physics 100 Lecture Note 12  Temperature scales and conversions Exercise ▪ The three major units used to measure temperature are Kelvin (K), which is the standard scientific unit, centigrade or Celsius (C ̊ ), and Fahrenheit (F ̊ ). ▪ The kelvin and the centigrade scales have the same steps, but different zeroes; they are related by 𝑇𝐾 = 𝑇𝐶 + 273.15 ▪ And the centigrade and Fahrenheit are related by the relation 9 𝑇𝐹 = 𝑇𝐶 + 32 5 ▪ To find the centigrade from Fahrenheit needs the above equation to be solved by 𝑇𝐶 Physics 100 Lecture Note 13 Example 1 ▪ Convert 20̊ C into Fahrenheit 9 9 𝑇𝐹 = 5 𝑇𝐶 + 32 = 𝑇𝐹 = 5 × 20 + 32 = 36 + 32 =68̊ F Example 2 ▪ Convert - 49̊ F into centigrade 5 5 𝑇𝐶 = 9 (𝑇𝐶 −32) = 9 × (−49 − 32) = −45 ̊C Examples ▪ Convert - 40̊ F into centigrade ▪ Convert 298̊ K into centigrade and Fahrenheit Physics 100 Lecture Note 14  Heat Heat: Internal energy transferred from one thing to another due to a temperature difference Internal energy in transit Flow of internal energy: From a high-temperature substance to a low-temperature substance until thermal equilibrium is reached Internal energy never flows unassisted from a low-temperature to a high- temperature substance Physics 100 Lecture Note 15  Heat If a red-hot spoon is immersed in warm water, the direction of heat flow will be from the A. warm water to the red-hot spoon. B. red-hot spoon to the warm water. C. There will be no heat flow. D. Not enough information. Physics 100 Lecture Note 16  Thermal Expansion Thermal expansion: ▪ Due to rise in temperature of a substance, molecules jiggle faster and move farther apart. ▪ Most substances expand when heated and contract when cooled: ▪ Railroad tracks laid on winter days expand and can buckle in hot summer. ▪ Warming metal lids on glass jars under hot water loosens the lid by more expansion of the lid than the jar. Plays a role in construction and devices such as: Use of reinforcing steel with the same rate of expansion as concrete—expansion joints on bridges. Gaps on concrete roadways and sidewalks allow for concrete expansion in the summer and contraction in the winter. Physics 100 Lecture Note 18 Physics 100 Lecture Note 19 Physics 100 Lecture Note 20 Physics 100 Lecture Note 21 Physics 100 Lecture Note 22  How heat flows from between places Heat flow mechanism Heat flow from one place to another according to one of the following mechanisms: ▪ Convection: Gas molecules that are heated collide with other molecules and transfer energy which in turn pass the energy to others. After a while the heat spreads through the gas ▪ Conduction: if you heat one side of a metal, heat quickly spreads through the whole metal. this way of heat transmission is called conduction. ▪ Radiation: Heat and light from the sun travel 150 million kilometers of empty space to reach us Heat from sun travels as electromagnetic waves Physics 100 Lecture Note 23  Radiation The surface of Earth loses energy to outer space due mostly to A. conduction. B. convection. C. radiation. D. radioactivity. Answer C. radiation. Explanation: Radiation is the only choice, given the vacuum of outer space. Physics 100 Lecture Note 24  Pressure ▪ If gas molecules are confined in a container, they bounce off of the walls of the container ▪ Each time a molecule bounces off, it pushes the wall of the container outward ▪ We say the gas molecules exert a pressure on the container surface Definition of pressure ▪ Pressure is the force on a surface divided by the area of the surface 𝐹𝑜𝑟𝑐𝑒 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝐴𝑟𝑒𝑎 Or symbolically 𝐹 𝑃= 𝐴 Where A is the area of surface the force pushes, and F is the force ▪ The unit of pressure comes from the units of force over the unit of area and it is called Pascal (Pa for short); 1Pa = 1N/ 𝑚2 Physics 100 Lecture Note 25  Examples of Pressure Force/Large Area = High Pressure Force/Small Area = High Pressure (you can see how the pencil tip goes (you can see how the pencil tip goes into into the skin the skin Physics 100 Lecture Note 26 Example 1 ▪ A hydraulic system whose surface area is 0.1𝑚2 lifts a 1000kg mass. How much pressure is exerted on the surface of the hydraulic system? 𝐹 1000×10 𝑃=𝐴= =100,000Pa 0.1 This is how much pressure the atmosphere exerts on the surface Example 2 ▪ The atmosphere exerts 101250 Pa on surfaces. How much force does the atmosphere exert on tabletop whose area is 1𝑚2 F = PA = 101250×1 = 101250N ▪ This is a huge force! Why doesn’t the table crack or crumble? Physics 100 Lecture Note 27  Heating a gas container ▪ Consider a closed container with atomic gas at room temperature inside it ▪ At room temperature the atoms have very high speeds (more than 500 m/s) ▪ At any moment will be many of their atoms bounce off the container walls ▪ Each atom that bounces off a container wall will exert an outward force on the wall ▪ At any moment, the small forces exerted on the container walls add up to a larger force ▪ This force divided by the area of the total surface of the walls creates pressure ▪ If the container is heated, the atoms will move faster and bounce off the wall harder, creating higher pressure on the walls ▪ Conclusion: the pressure of a gas is directly proportional to its temperature Physics 100 Lecture Note 28  Inflating a balloon ▪ We saw above that heating the gas in the container is one way to increase pressure. ▪ Another way that the pressure inside a container can increase is by adding more gas in it ▪ This is what we do when we inflate balloons; we add more air in them ▪ More gas particles with the same average energy (temperature or speed) increases the number of particles bouncing of the walls at any moment ▪ More particles bouncing off means larger overall force on the container wall. ▪ This means that pressure in the container will be higher ▪ Conclusion: the pressure of a gas is directly proportional to the number of particles in the container Physics 100 Lecture Note 29  Squeezing a balloon ▪ We saw above that heating and increasing the number of particles in a container both increase the pressure on the container walls ▪ Another way that the pressure inside a container can increase is by decreasing the volume ( squeeze the balloon) ▪ Smaller volume means less space for the particles to stay before they collide with the walls ▪ As a result, the particles will collide with the wall more frequently, exerting a higher pressure ▪ Smaller volume (without change in the average energy or the number of particles) leads to higher pressure in the container ▪ Conclusion: the pressure of a gas in a container is inversely proportional to the volume Physics 100 Lecture Note 30  The formula for the ideal gas law is: PV = nRT P =pressure V = volume n = number of moles of gas R = ideal or universal gas constant = 0.08 L atm / mol K T = Absolute Temperature in Kelvin Physics 100 Lecture Note 31  Examples ▪ Pressure cooking is the process of cooking food using water or other cooking liquid, in a sealed vessel ▪ As pressure cooking cooks food faster than conventional cooking methods, it saves energy ▪ Pressure is created by boiling a liquid, such as water or broth, inside the closed pressure cooker ▪ The trapped steam increases the internal pressure and allows the temperature to rise Physics 100 Lecture Note 32 ▪ How can heat affect the state of an object? The state of a substance depends on the speed of its particles. Adding energy in the form of heat to a substance can result in a change of state. Removing energy in the form of heat from a substance can also result in a change of state. Add energy in the form of heat or subtract energy in the form of heat. Physics 100 Lecture Note 33 THERMODYNAMICS: the science of energy, specifically heat and work, and how the transfer of energy effects the properties of materials. Thermodynamics: "Thermo":Greek therme heat "Dynamics":Greek dynamikos powerful Physics that deals with the mechanical action or relations between heat and work Example: Heat to work - Engine Physics 100 Lecture Note 34  1st Law of Thermodynamics The total sum of all energy in an isolated system will never increase or decrease. “Law of conservation of energy.” Energy cannot be created or destroyed, only transfer forms. (H) Change of internal energy = (Q) Heat added to the system – (W) Work done by the system Physics 100 Lecture Note 35  Heat, work and internal energy ▪ The internal energy of a system is the amount of energy a system possesses as a result of the motion of particles it is composed of any change of internal energy of a system is accompanied by work and heat. ▪ The energy released by the food we eat allows us to move around (work) and part of it gets released as heat ▪ A plant absorbs sunlight and turns part of radiant energy into chemical energy ▪ Since energy can neither be created nor destroyed, the change of internal energy is always equal to the work done and heat emitted or absorbed ▪ This is the essence of the first law of thermodynamics Physics 100 Lecture Note 36  2ns law of thermodynamics If two objects are not the same temperature then: Heat will always flow from high to low temperatures. Hot objects will decrease in temperature and cold objects will increase in temperature until they are both the same temperature. Heat can never pass spontaneously from a cold to a hot body. As a result of this fact, natural processes that involve energy transfer must have one direction, and all-natural processes are irreversible. Heat flows from hot to cold. Machines cannot be 100% efficient. Physics 100 Lecture Note 37  Natural heat flow ▪ Heat always flows between objects and from place to place ▪ When you touch a cold object ▪ When you touch a hot object ▪ When you touch a hot object, heat flows from the object to your finger When nature is left alone, heat always flows from higher temperature systems to lower temperature ones Physics 100 Lecture Note 38 Entropy Physics 100 Lecture Note 39  Entropy Increasing Entropy Solids Liquids Solutions Gases Fewer Particles More Particles Physics 100 Lecture Note 40  Order vs disorder ▪ System has a low degree of disorder ▪ System has a high degree of ▪ Speed and direction are the same disorder and soldiers are lined up ▪ Speed and are different Physics 100 Lecture Note 41  More examples of entropy Entropy is randomness. Which is more random? A or B? A B Physics 100 Lecture Note 42  More examples of entropy 2nd Law of Thermodynamics says that nature always goes from order to disorder. A B Physics 100 Lecture Note 43  More examples of entropy In nature, do you move from A to B or B to A? A B Physics 100 Lecture Note 44  More examples of entropy 2nd law says that nature always, always moves from A to B and never from B to A. A B Physics 100 Lecture Note 45  Entropy can be lowered by doing work on the system. You can stack the bricks back up by hand. Physics 100 Lecture Note 46 More examples of entropy Physics 100 Lecture Note 47  More examples of entropy - On a large scale, the ice “looks” more disordered. - On a small scale, the solid phase severely limits where the molecules could be. - The ice crystal molecules are much more ordered than the free-moving liquid water molecules. Physics 100 Lecture Note 48  Heat pumps and heat engines ▪ A heat pump is a device that reverses the direction of heat flow. ▪ A heat pump does heat flow what water pumps do to water flow. ▪ Air conditioners and refrigerators are heat pumps. ▪ Heat engines, on the other hand, convert heat into work. ▪ Thermal energy (heat) is a form of energy, so like any other type of energy, it can be converted to work. ▪ So a heat engine is any device that can use thermal energy to do work. ▪ Internal combustion engines (like car engines) are good examples of heat engines that turn thermal energy into work. Physics 100 Lecture Note 49