Work, Heat, and the First Law of Thermodynamics

Work, heat, and the first law of thermodynamics 19.1 It’s All About Energy ¢K = Wc + Wdiss + Wext tells us that the kinetic energy of a system of particles is changed when forces do work on the partners by pushing or pulling them through a distance (1) W(c) is the work done by conservative forces. This work can be represented as a change in the systems potential energy: ¢U = ¡Wc (2) W(diss) is the work done by friction-like dissipate forces within the system. This work increases the system's thermal energy: ¢Eth = ¡Wdiss (3) W(ext) is the work done by external forces that originate in the environment. The push of a piston rod would be an external force Modified equation ¢K + ¢U + ¢Eth = Wext 1 Earlier we were interested in learning now kinetic and potential energy were transformed into each other and, where there is friction, into thermal energy. Now we want to focus on how energy is transferred between the system and its environment when W(ext) is not zero Energy Transfer The point of this example is that the energy transferred to a system can go entirely to the system's mechanical energy, entirely to its thermal energy, or (imagine dragging the object up an incline) some combination of the two The Missing Piece: Heat You can transfer energy into a system by the mechanical process of doing work on the system Work is energy transferred in a mechanical interaction, but that is not the only way a system can interact with its environment Energy can also be transferred between the system and the environment if they have a thermal interaction. The energy transferred in a thermal interaction is called heat ¢Esys = ¢Emech + ¢Eth = W + Q 19.2 Work in Ideal-Gas Processes Work is the energy transferred between a system and the environment when a net force acts on the system over a distance The process itself is a mechanical interaction, meaning that the system and the environment interact via macroscopic pushes and pulls A system is in mechanical equilibrium if there is no net force on the system The sign of the work is not just an arbitrary convention, nor does it have anything to do with the choice of coordinate system In contrast to the mechanical energy or the thermal energy, work is not a state variable. Instead, work is the amount of energy that moves between the system and the environment during a mechanical interaction To prevent the pressure from blowing the piston out of the cylinder, there must be an equal but opposite (Fext)x = ¡ (Fgas)x = ¡pA external force If we allow the gas to change in a slow, quasi-static process from an initial volume to a final volume, the Z V total work done by the environment would be: Wext = ¡ pdV f Vi Work is an energy transfer, but the piston's energy is not changing. It is in equilibrium, with equal forces exerted on both faces The piston is merely a movable boundary of the gas, so the work is done by the environment on the gas. When a gas expands or contracts, energy is transferred between the gas and the environment However, the work that appears in the energy principle, and now in the laws of thermodynamics, is W(ext), the work done by the environment - either positive or negative - on the system, and that is the work that will appear in our equations When a gas is compressed, it is often said that "work is done on the gas". This is a situation with W(ext)> 0 and W(gas) < 0. When a gas expands, it is often said that "work is done by the gas". It simply means that W(gas) > 0 and so, in this case, you would use W(ext) < 0 Work is the negative area under the pV curve between the initial volume and the final volume Work for different processes: W = 0 (isochoric) W = ¡p¢V (isobaric) W = ¡nRT ln µ Vf Vi ¶ Work depends on the path The work done during an ideal-gas process depends on the path followed through the pV diagram For an ideal-gas process, the "path" is a sequence of thermodynamic states on a pV diagram. It is a figurative path because we can draw a picture of it on a pV diagram, but it is not a literal path (isothermal) 19.3 Heat Joule found that you can raise the temperature of a beaker of water by two entirely different means: (1) heating it with a flame, or (2) doing work on it with a rapidly spinning paddle wheel The final state of the water is exactly the same in both cases. This implies that heat and work are essentially equivalent. In other words, heat is not a substance, instead, heat is energy Thermal Interactions To be specific, heat is the energy transferred between a system and the environment as a consequence of a temperature difference between them Instead, energy is transferred when the faster molecules in the hotter object collide with the slower molecules in the cooter object. On average, these collisions cause the faster molecules to lose energy and the slower molecules to gain energy The process itself, whereby energy is transferred between the system and the environment via atomiclevel collisions, is called a thermal interaction A system is in thermal equilibrium with the environment, or two systems are in thermal equilibrium with each other, if there is no temperature difference Like work, heat is not a state variable. That is, heat is not a property of the system. Instead, heat is the amount of energy that moves between the system and the environment during a thermal interaction Heat, Temperature, and Thermal Energy Thermal energy is an energy of the system due to the motion of its atoms and molecules and the stretching/compressing of spring-like molecular bonds The system's thermal energy continues to exist even if the system is isolated and not interacting thermally with its environment Heat is energy transferred between the system and the environment as they interact Q = 0 if a system does not interact thermally with its environment Heat may cause the system's thermal energy to change, but that doesn't make head and thermal energy the same Temperature is a state variable that quantifies the "hotness" or "coldness" of a system A temperature difference is a requirement for a thermal interaction in which heat energy is transferred between the system and the environment Observing the system tells us nothing about the process by which energy enters or leaves the system 19.4 The First Law of Thermodynamics Work and heat, two ways of transferring energy between a system and the environment, cause the system’s energy to change ¢Eth = W + Q (first law of thermodynamics) The first law of thermodynamics is the basis for a more general energy model, the thermodynamic energy model, in which work and heat are on an equal footing Thermodynamic energy model Work and heat are energies transferred between the system and the environment Work is energy transferred in a mechanical interaction Heat is energy transferred in a thermal interaction The first law of thermodynamics says that transferring energy to the system changes the system's thermal energy ¢Eth = W + Q W and Q > 0 for energy added W and Q < 0 for energy removed Limitations: model fails if the system's mechanical energy also changes Work or heat that changes the system's thermal energy also changes other state variables, such as pressure, volume, or temperature Three Special Ideal-Gas Processes The first law of thermodynamics is an additional law that gases must obey, one focused specifically on the process by which a gas is changed Isothermal process (change of thermal energy = 0): If the temperature of a gas doesn't change, neither does its thermal energy. In this case, the first law is W +Q = 0 An isothermal process exchanges work and heat (one entering the system, the other leaving) without changing the gas temperature Isochoric process (W = 0): An isochoric process has no change in volume; thus no work is done and the first law can be written as the change in thermal energy equals the heat This is a process in which the system is mechanically isolated from its environment Heating (or cooling) the gas increases (or decreases) its thermal energy, so the temperature goes up (or down) Adiabatic process (Q = 0): A process in which no heat is transferred - perhaps the system is extremely well insulated - is called an adiabatic process But just because there's no heat does not mean that the temperature remains constant. Compressing an insulated gas - a mechanical interaction with W > 0 - raises its temperature 19.5 Thermal Properties of Matter Heat and work are equivalent in the sense that the change of the system is exactly the same whether you transfer heat energy to it or do an equal amount of work on it Temperature Change and Specific Heat The amount of energy that raises the temperature of 1 kg of a substance by 1 K is called the specific heat of that substance If energy c is required to raise the temperature of 1 kg of a substance by 1 K, then energy Mc is needed to raise the temperature of mass M by 1 K and (Mc) delta T is needed to raise the temperature of mass M by delta T ¢Eth = M c¢T The change of thermal energy can be either positive (thermal energy increases as the temperature goes up) or negative (thermal energy decreases as the temperature goes down) In other words, we can change the system's temperature either by heating it or doing an equivalent amount of work on it (temperature change) Q = M c¢T It takes more energy to change the temperature of a substance with a large specific heat than to change the temperature of a substance with a small specific heat The molar specific heat is the amount of energy that raises the temperature of 1 mol of a substance by 1 K… Q = nC¢T Phase Change and Heat of Transformation The slope of the graph depends inversely on the system's specific heat. A constant specific heat implies a constant slope and this a linear graph But there are times, shown as horizontal line segments, during which heat is being transferred to the system but the temperature isn't changing. These are phase changes The thermal energy continues to increase during a phase change, but the additional energy goes into breaking molecular bonds rather than speeding up the molecules A phase change is characterized by a change in thermal energy without a change in temperature The amount of heat energy that causes 1 kg of a substance to undergo a phase change is called the heat of transformation of that substance Two specific heats of transformation are the heat of fusion, the heat of transformation between a solid and a liquid, and the heat of vaporization, the heat of transformation between a liquid and a gas Melting breaks just enough molecular bonds to allow the system to lose rigidity and flow. Vaporization breaks all bonds completely and sends the molecules flying apart 19.6 Calorimetry Insulation prevents any heat energy from being transferred to or from the environment, so energy conservation tells us that any energy leaving the hotter system must enter the colder system 19.7 The Specific Heats of Gases Gases are harder to characterize because the heat required to cause a specified temperature change depends on the process by which the gas changes state Q = nCV¢T (temperature change at constant volume) Q = nCP ¢T (temperature change at constant pressure) C(P) and C(V) First, the molar specific heats of monatomic gases are all alike. And the molar specific heats of diatomic gases, while different from monatomic gases, are again very nearly alike The relationship between C(V) and C(P) hinges on one crucial idea: the change in the thermal energy of a gas, is the same for any two processes that have the same change in temperature The thermal energy of a gas is associated with temperature, so any process that changes the gas temperature from an initial temperature to a final temperature has the same change of thermal energy as any other process that goes from initial to final temperature The system’s thermal energy changes in response to energy added or removed from the system, but the response of the gas is the same whether you heat the system, do work on the system, or do some combination of both Cp = Cv + R ¢Eth = nCv¢T (any ideal-gas process) The change in thermal energy when the temperature changes by delta T is the same for any process The heat required to bring about the temperature change depends on what the process is In an isochoric process, where W = 0, all the heat input is used to increase the gas temperature. But in an isobaric process, some of the energy that enters the system as heat then leaves the system as work (W < 0) done by the expanding gas Heat Depends on the Path Even though the initial and final States are the same, the heat added during these two processes is not the same The thermal energy is a state variable. That is, its value depends on the state of the gas, not the process by which the gas arrived at that state The heat added or removed during an ideal-gas process depends on the path followed through the pV diagram Adiabatic Processes In practice, there are two ways than an adiabatic process can come about. First, a gas cylinder can be completely surrounded by thermal insulation, such as thick pieces of styrofoam. Second, the gas can be expanded or compressed very rapidly in what we call adiabatic expansion or an adiabatic compression A process that takes place faster than the heat can be transferred is adiabatic Compressing a gas adiabatically (W > 0) increases the thermal energy. Thus an adiabatic compression raises the temperature of a gas A gas that expands adiabatically (W < 0) gets colder as its thermal energy decreases. Thus an adiabatic expansion lowers the temperature of a gas (adiabatic process) W = nCv¢T An adiabatic process moves along an adiabat in the same way than an isothermal process moves along an isotherm. 19.8 Heat-Transfer Mechanisms Conduction The temperature difference causes heat energy to be transferred from the hot side to the cold side in a process known as conduction A material with a larger cross section transfers more heat, while a thicker material, increasing the distance L between the hot and cold sources, decreases the rate of heat transfer dQ A = k ¢T dt L The quantity k, which characterizes whether the material is a good conductor of heat or a poor conductor, is called the thermal conductivity of the material Air and other gases are poor conductors of heat because there are no bonds between adjacent molecules Convection Air is a poor conductor of heat, but thermal energy is easily transferred through air, water, and other fluids because the air and water can flow This transfer of thermal energy by the motion of a fluid - the well known idea that "heat rises" - is called convection