1Chapters 17 and 18 Phases and the Laws of Thermodynamics2Overview• Ideal Gases • Kinetic Theory • Latent Heat • The First and Second Laws of Thermodynamics • Thermal Processes • Heat Engines and the Carnot Cycle • Entropy • The Third Law of Thermodynamics317-1 Ideal Gases• Gases are the easiest state of matter to describe… - All ideal gases exhibit similar behavior. • An ideal gas is one that is thin enough, that the interactions between molecules can be ignored.4If volume of an ideal gas is held constant, we find that the pressure increases with temperature:17-1 Ideal Gases5If volume and temperature are kept constant, but more gas is added (such as in inflating a tire or basketball), the pressure will increase:17-1 Ideal Gases6Finally, if the temperature is constant and the volume decreases, the pressure increases:17-1 Ideal Gases717-1 Ideal GasesCombining all three observations, we getwhere k is called the Boltzmann constant:Rearranging:817-1 Ideal GasesExperimentally, the number of entities (atoms or molecules) in a mole is given by Avogadro’s number:Therefore, n moles of gas will contain molecules:917-1 Ideal GasesAvogadro’s number and the Boltzmann constant can be combined to form the universal gas constant and an alternative equation of state:1017-2 Kinetic TheoryKinetic theory relates microscopic quantities (position, velocity) to macroscopic ones (pressure, temperature). Assumptions: 1.N identical molecules of mass m are inside a container of volume V; each acts as a point particle. 2. Molecules move randomly and always obey Newton’s laws. 3. Collisions with other molecules and with the walls are elastic.1117-2 Kinetic TheoryPressure is the result of collisions between the gas molecules and the walls of the container.Depends on the mass and speed of the molecules, and on the container size:1217-2 Kinetic TheoryNot all molecules in a gas will have the same speed; their speeds are represented by the Maxwell distribution, and depend on the temperature and mass of the molecules.1317-2 Kinetic TheoryReplace the speed in the previous expression for pressure with average speed: Considering the other two directions,Pressure in gas is proportional to the average kinetic energy of its molecules…1417-2 Kinetic TheoryComparing this expression with the ideal gas law allows us to relate average kinetic energy and temperature:The square root of is called the root mean square (rms) speed…1517-2 Kinetic TheorySolving for the rms speed gives:1617-2 Kinetic TheoryRms speed is slightly greater than the most probable speed and the average speed.1717-2 Kinetic Theory• Internal energy of ideal gas is sum of the kinetic energies of all its molecules. • In the case where each molecule consists of a single atom, this is:1817-5 Latent Heats• When two phases coexist, the temperature remains the same even if a small amount of heat is added. • Instead of raising the temperature, the heat goes into changing the phase of the material – melting ice, for example.1917-5 Latent Heats• Heat required to convert from one phase to another is called the latent heat. •Latent heat, L, is the heat that must be added/removed to one kilogram of a substance to change its phase • During the conversion process, the temperature of the system remains constant.2017-5 Latent Heats• Latent heat of fusion: heat needed to go from solid to liquid • Latent heat of vaporization: heat needed for liquid to gas.2118-2 The First Law of ThermodynamicsFirst law of thermodynamics is a statement of the conservation of energy. If a system’s volume is constant, and heat is added, its internal energy increases.2218-2 The First Law of ThermodynamicsIf a system does work on the external world, and no heat is added, its internal energy decreases.2318-2 The First Law of ThermodynamicsCombining these gives first law of thermodynamics. The change in a system’s internal energy is related to the heat Q and the work W as follows:Vital to keep track of the signs of Q and W.2418-3 Thermal Processes• We will assume that all processes we discuss are quasi-static: - They are slow enough that the system is always in equilibrium…. • We also assume they are reversible: - For a process to be reversible, it must be possible to return both the system and its surroundings to exactly the same states they were in before the process began.2518-3 Thermal ProcessesIdealized reversible process: • The gas is compressed; the temperature is constant, so heat leaves the gas… • As the gas expands, it draws heat from the reservoir, returning the gas and the reservoir to their initial states.2618-3 Thermal ProcessesWork done by an expanding gas, constant pressure:2718-3 Thermal ProcessesIf the volume stays constant, nothing moves and no work is done.2818-3 Thermal ProcessesIf the temperature is constant, the pressure varies inversely with the volume.2918-3 Thermal ProcessesThe work done is the area under the curve:3018-3 Thermal ProcessesAn adiabatic process: • One in which no heat flows into or out of the system. •The adiabatic P-V curve is similar to the isothermal one, but is steeper. • One way to ensure that a process is adiabatic is to insulate the system.3118-3 Thermal ProcessesHere is a summary of the different types of thermal processes:3218-5 The Second Law of Thermodynamics• We observe that heat always flows spontaneously from a warmer object to a cooler one… - This direction of heat flow is one of the ways of expressing the second law of thermodynamics: “When objects of different temperatures are brought into thermal contact, the spontaneous flow of heat that results is always from the high temperature object to the low temperature object. Spontaneous heat flow never proceeds in the reverse direction.”3318-6 Heat Engines and the Carnot CycleHeat engine is a device that converts heat into work. A classic example is the steam engine. • Fuel heats the water • Vapor expands and does work against the piston • Vapor condenses back into water again and the cycle repeats.3418-6 Heat Engines and the Carnot CycleAll heat engines have: • High-temperature reservoir • Low-temperature reservoir • Cyclical engine3518-6 Heat Engines and the Carnot Cycle•An amount of heat Qh is supplied from the hot reservoir to the engine during each cycle…. •Of that heat, some appears as work, and the rest, Qc, is given off as waste heat to the
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