2024 Physics Lecture Notes PDF

LECTURE 9 Internal energy Thermodynamic systems The zeroth law of thermodynamics The first law of thermodynamics Reading: Cutnell & Johnson sections 14.3, 15.1-15.3 1 Internal energy Internal energy U of a substance...

LECTURE 9 Internal energy Thermodynamic systems The zeroth law of thermodynamics The first law of thermodynamics Reading: Cutnell & Johnson sections 14.3, 15.1-15.3 1 Internal energy Internal energy U of a substance = sum of all the energies of the individual atoms or molecules – Translational kinetic energy – Rotational energy – Vibrational energy (kinetic and potential) – May be others as well (e.g., in a magnetic field there may be magnetic energy, etc.) 2 Internal energy *** Monatomic gas ***: Atoms assumed to be point-like – Mass concentrated at that point No rotational kinetic energy – No chemical bonds between atoms No vibrational energy – Internal energy U is sum of the translational kinetic energies only 3 Internal energy *** Monatomic gas ***: For N particles: "1 2 % U = N $ mv rms ' #2 & Using the microscopic definition of temperature, 1 2 3 € mv rms = kT 2 2 internal energy becomes: "3 % € U = N $ kT ' #2 & 4 Internal energy Can use moles n instead of no of particles N: 3 3 U = N kT = nRT 2 2 – For a monatomic gas! In fact, the internal energy is proportional to the € Kelvin temperature for any ideal gas – Monatomic, diatomic, etc. But: the constant of proportionality can be different! – Don’t use the exact equation above if it’s not a monatomic gas!! 5 Thermodynamics Branch of physics concerned with heat and its relation to other forms of energy and work – “thermo-”: heat – “dynamics”: the mechanics of forces and the motion of objects Looks at the bulk, or macroscopic, properties of objects – Temperature, internal energy, pressure, volume… 6 Thermodynamics Photo: https://en.wikipedia.org/wiki/Internal_combustion_engine (Czmarlin) Ex: car engine (conventional combustion engine) – Fuel burned at high temperature – Some of its internal energy is used for work: driving the pistons up and down – Excess heat removed by the cooling system to prevent overheating 7 Thermodynamic system System = the object (or collection of objects) that is the focus of attention Surroundings = everything else in the environment Heat may be transferred between the system and the surroundings Work may be done by the system on the surroundings, or vice versa 8 Thermodynamic system Walls of some kind separate the system from the surroundings Diathermal walls permit heat to flow through them – “Dia-” means “through” Adiabatic walls are perfectly insulating – “Adiabatic” means no transfer of heat 9 The zeroth law of thermodynamics Two systems individually in equilibrium with a third system are in thermal equilibrium with each other 10 The zeroth law of thermodynamics Two systems individually in equilibrium with a third system are in thermal equilibrium with each other Thermal equilibrium: No heat flow between the two systems when they are brought into contact 11 The zeroth law of thermodynamics Two systems individually in equilibrium with a third system are in thermal equilibrium with each other Temperature: There is no heat flow between two systems that are in thermal contact and have the same temperature 12 The zeroth law of thermodynamics Part (a): The containers have insulating (e.g., adiabatic) walls, and they have the same temperature Part (b): One wall of each container is replaced by a diathermal wall No flow of heat in part (b), even though diathermal walls would permit it Temperature is the indicator of thermal equilibrium 13 The zeroth law of thermodynamics C Thermometer: System A is in equilibrium with the thermometer System B is in equilibrium with the thermometer The thermometer is a third system: A and B are in thermal equilibrium with each other 14 The zeroth law of thermodynamics Two systems individually in equilibrium with a third system are in thermal equilibrium with each other Zeroth law à establish temperature as the indicator of thermal equilibrium – All parts of a system must be in thermal equilibrium if the system is to have a single temperature – No heat flow within a system that is in thermal equilibrium 15 Example: The zeroth law in practice Which one of the following situations is described by the zeroth law of thermodynamics? a) An air conditioner transfers heat from the inside of a house to the outside of the house. b) A monatomic gas is held within a container that has a moveable piston. The gas absorbs heat from the surroundings and expands at constant pressure and temperature. c) A container with adiabatic walls holds boiling water. A thermometer is calibrated by inserting it into the boiling water and allowing it to reach thermal equilibrium with the water. d) A pot contains oil at 175°C. When frozen sliced potatoes are dropped into the oil, heat is transferred from the oil to the potatoes. e) A physicist removes energy from a system in her laboratory until it reaches a temperature of 3 × 10-10 K, a temperature very close to (but still greater than) absolute zero. 16 The first law of thermodynamics Forces can do work; work can change the kinetic and potential energy of an object – Ex: Colliding atoms or molecules of a substance exert forces on each other, and on the walls to the surroundings – Gives them kinetic and potential energy – Internal energy = sum of these and other molecular energies When a substance participates in a process involving work and/or transfer of heat, its internal energy can change as a result The first law relates the change of internal energy to the heat transferred and the work done 17 The first law of thermodynamics: heat A system gains heat Q (no other effect occurring): Change in internal energy: ΔU = U f − U i = Q Conservation of energy € Sign convention: Heat Q is positive when the system gains heat, and negative when the system loses heat 18 The first law of thermodynamics: work A system does work on its surroundings (no heat flow): Change in internal energy: ΔU = U f − U i = −W Conservation of energy € Sign convention: Work W is positive when it is done by the system, and negative when it is done on the system – NB The opposite sign convention exists, too!! Not used in this course 19 The first law of thermodynamics: work The two conventions ΔU = U f − U i = −W ∆𝑈 = 𝑈( − 𝑈) = +𝑊 Engineers tend to consider work Physicists tend to consider work done by the system as positive. done on the system as positive. When designing a system, engineers When considering a system, doing want to know what work the system something that adds energy to the will do. system is considered positive. ∆𝑈 = 𝑄 − 𝑊 ∆𝑈 = 𝑄 + 𝑊 Work done BY the system is Work done ON the system is positive. positive. The main textbook for this module Some other textbooks may use this (Cutnell & Johnson) convention. Make sure you check. uses this convention 20 The first law of thermodynamics: work The two conventions ΔU = U f − U i = −W ∆𝑈 = 𝑈( − 𝑈) = +𝑊 Engineers tend to consider work Physicists tend to consider work done by the system as positive. done on the system as positive. When designing a system, engineers When considering a system, doing want to know what work the system something that adds energy to the will do. system is considered positive. ∆𝑈 = 𝑄 − 𝑊 ∆𝑈 = 𝑄 + 𝑊 Work done BY the system is Work done ON the system is positive. positive. The main textbook for this module Some other textbooks may use this (Cutnell & Johnson) convention. Make sure you check. uses this convention 21  The first law of thermodynamics Combine the two: Change in internal energy due to heat flow and work: ΔU = U f − U i = Q − W Conservation of energy € Sign convention: – Heat Q is positive when the system gains heat, and negative when the system loses heat – Work W is positive when it is done by the system, and negative when it is done on the system NB The other sign convention exists, too!! 22 Example: Positive and negative work In part (a) of the figure, the system gains 1500 J of heat, and 2200 J of work is done by the system on its surroundings. In part (b), the system also gains 1500 J of heat, but 2200 J is done on the system. In each case, determine the change in internal energy of the system. 23 Example: An ideal gas The temperature of three moles of a monatomic ideal gas is reduced from Ti = 540 K to Tf = 350 K by two different methods. In the first method, 5500 J of heat flows into the gas, whereas in the second, 1500 J flows into it. In each case, find (a) the change in internal energy and (b) the work done by the gas. 25 SUMMARY Internal energy of a gas is proportional to Kelvin temperature – For a monatomic gas: 3 3 – Different constant of proportionality U = N kT = nRT (not 3/2) if diatomic or other gas 2 2 (Thermodynamic) system = the object of focus Surroundings = everything else – Heat may be transferred into or out of the system – Work may be done on or by the system € Zeroth law of thermodynamics: – Two systems individually in equilibrium with a third system are in thermal equilibrium with each other First law of thermodynamics: ΔU = U f − U i = Q − W – A statement of conservation of energy – Note sign convention! € + + - + 28