Presentation on theme: "Work in Thermodynamic Processes We are now ready to combine the energy transfer mechanism of heat with another mechanism: work –We will focus our discussion."— Presentation transcript:
Work in Thermodynamic Processes We are now ready to combine the energy transfer mechanism of heat with another mechanism: work –We will focus our discussion on work done on a gas –Important in discussion of how system gets from one state to another (described by state variables P, T, V, n, U ) –Will provide connection between microscopic and macroscopic energy transfer mechanisms In Chap. 5 we spoke about work done by forces on objects undergoing a displacement Now we will talk about the work done on a gas by the environment W (or by gas on environment W env ) –Work done on gas ( W ) can be positive, negative, or zero – W = 0 when no mechanical action taking place – W = –W env –Work influences internal energy
Work in Thermodynamic Processes Work done by a gas on a piston in a cylinder: W env = F y = PA y = P V = P(V f – V i ) –When the piston moves inward, V f < V i and W env < 0 –When the piston moves outward, V f > V i and W env > 0 –When piston doesnt move, W env = 0 Work done by the piston on the gas = W = –W env –When the piston moves inward, V f 0 –When the piston moves outward, V f > V i and W < 0 –When piston doesnt move, W = 0 (from University Physics, 11 th Ed.)
Work in Thermodynamic Processes This expression can only be used if the pressure remains constant during the expansion or compression –This is called an isobaric (constant pressure) process (same Greek root as barometer) If the pressure changes, the average pressure may be used to estimate the work done If pressure and volume are known at each step of the process, a PV diagram helps visualize process with curves (paths) connecting initial and final states The area under the curve on a PV diagram is equal in magnitude to the work done on a gas (W) –True whether or not P remains constant – W is positive (negative) when volume decreases (increases)
PV Diagrams For a gas being compressed at constant pressure: For a gas being compressed with varying pressure: The work done depends on the particular path (shaded area represents work done on the gas; here W > 0 ) (shaded area, the area under the curve, represents work done on the gas) (same initial and final states, but work done is different in each case)
Other Thermodynamic Processes Isovolumetric (or isochoric) –Volume stays constant –For example, maintain constant piston position –Vertical line on the PV diagram –No work done on gas Isothermal –Temperature stays constant –Heat flows between the system and a reservoir to keep the systems temperature constant –For example, keep oven temperature constant Adiabatic –No energy exchanged with the surroundings via heat –For example, provide excellent insulation for system –Or, process occurs so quickly that there is no time for heat to flow in or out of system PV Processes Interactive
Example Problem #12.5 Solution (details given in class): (a)– 810 J (b)– 507 J (c)– 203 J A gas expands from I to F along the three paths indicated in the figure. Calculate the work done on the gas along paths (a) IAF (b) IF, and (c) IBF.
First Law of Thermodynamics Both work and heat can change the internal energy of a system –Work can be done on a rubber ball by squeezing it, stretching it, or throwing it onto a wall –Energy can flow to the ball via heat by leaving it out in the sun or putting it into a hot oven These 2 methods of increasing the internal energy of a system lead to the first law of thermodynamics: –The change in internal energy of a system is equal to the heat flow into the system plus the work done on the system – U = internal energy change of system – Q = energy transferred to system by heat from the outside – W = work done on the system (really a statement of energy conservation!)
Sign Conventions for First Law QuantityDefinitionMeaning of + signMeaning of – sign Q Energy transferred by heat flow Heat flow into the system Heat flow out of the system W WorkWork done on the system Work done by the system U Internal energy change Internal energy increase Internal energy decrease In–class example – Fill in the boxes with +, –, or 0: SituationSystem QW U (a) Rapidly pumping up bicycle tireAir in the pump (b) Pan of room-temperature water resting on a hot stove Water in the pan (c) Air leaking quickly out of a balloonAir rushing out of balloon
Applications of the First Law Isolated system: does not interact with its surroundings –No energy transfer takes place and no work is done –Internal energy of the isolated system remains constant – Q = W = U = 0 Cyclic process: originates and ends at the same state – U = 0 and Q = –W –The net work done per cycle by the gas is equal to the area enclosed by the path representing the process on a PV diagram (important for describing heat engines) PV diagram for an ideal monatomic gas confined in a cylinder by a movable piston undergoing a cyclic process
Applications of the First Law Isothermal process: constant- temperature process Consider ideal monatomic gas contained in cylinder with movable piston The cylinder and gas are in thermal contact with a large source of energy (reservoir) Allow energy to transfer into the gas by heat The gas expands (volume increases) and pressure falls while maintaining a constant temperature Since, U = 0 –Therefore U = 0 = Q + W –So W = – Q < 0 (system supplies work to outside world)
Applications of the First Law Adiabatic process: no energy transferred by heat –The work done is equal to the change in the internal energy of the system ( W = U ) –One way to accomplish a process with no heat exchange is to have it happen very quickly (mostly true in an internal combustion engine) –In an adiabatic expansion, the work done is negative and the internal energy decreases –For an ideal monatomic gas (see Chap. 10): Isovolumetric process: no change in volume, so W = 0 –The energy added to the system goes into increasing the internal energy of the system ( U = Q ) –Temperature will increase Isobaric process: no change in pressure – W = – P V, so U = Q – P V
The First Law and Human Metabolism The first law can be applied to living organisms The internal energy stored in humans goes into other forms needed by the organs and into work and heat –When we eat, we replenish our supply of internal energy The metabolic rate ( U / t) is directly proportional to the rate of oxygen consumption by volume –Basal metabolic rate (to maintain and run organs, etc.) is about 80 W (other rates shown in Table 12.4) The efficiency of the body is the ratio of the mechanical power output to the metabolic rate –What you get out divided by what you put in –Efficiencies range from about 20% (cycling) to 3% (shoveling)
Example Problem #12.16 Solution (details given in class): (a)12 kJ (b)–12 kJ A gas is taken through the cyclic process described by the figure. (a)Find the net energy transferred to the system by heat during one complete cycle. (b)If the cycle is reversed that is, the process follows the path ACBA what is the net energy transferred by heat per cycle?
Interactive Example Problem: Triangular Cyclic Process on a PV Diagram Simulation and solution details given in class. (ActivPhysics Online Exercise #8.13, copyright Addison Wesley publishing)
Heat Engines A heat engine is a device that converts internal energy to other useful forms, such as electrical or mechanical energy –Electrical power plants –Internal combustion engine in cars A heat engine carries some working substance through a cyclical process Energy is transferred from a source at a high temperature ( Q h ) Work is done by the engine ( W eng ) Energy is expelled to a source at a lower temperature ( Q c ) Example of piston steam engine (in-class movie): Animation
Heat Engine Since it is a cyclical process, its initial and final internal energies are the same –So, U = 0 = Q + W and Q = Q net = – W = W eng The work done by the engine equals the net energy absorbed by the engine –Therefore, The work is equal to the area enclosed by the curve of the PV diagram (if working substance is a gas) Thermal efficiency is defined as the ratio of the work done by the engine to the energy absorbed at the higher temperature (what you get divided by what you put in):
Second Law of Thermodynamics The efficiency of heat engines is addressed in the second law of thermodynamics: –No engine can have 100% efficiency Other statements and implications of the second law: –A system cannot convert heat solely into mechanical work –Heat never flows spontaneously from a colder body to a hotter body –It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter body –There is no such thing as a free lunch! Summary of 1 st and 2 nd laws: –1 st law: We cannot get more energy out than we put in –2 nd law: We cannot break even
Internal Combustion Engines An idealized model of the thermodynamic processes of a gas engine is called the Otto cycle –Intake stroke: Gas-air mixture drawn into cylinder (a b) –Compression stroke: Intake valve closes, mixture compressed (adiabatic compression; b c) –Ignition: Spark plug ignites mixture (heating at constant volume; c d) –Power stroke: Hot burned mixture pushes mixture down, doing work (adiabatic expansion; d e) –Cooling: Energy released via heat at constant volume (e b) –Exhaust stroke: Exhaust valve opens and burned mixture is pushed out of cylinder (b a) (from University Physics, 11 th Ed.) (from College Physics, Giambattista)
Heat Pumps: Refrigerators, Air conditioners Refrigerators –Energy is extracted from the cold reservoir (food cabin) and transferred to hot reservoir (kitchen) Air conditioner works on the same principle Both are examples of a heat pump (reverse heat engines) (from University Physics, 11 th Ed.) Heat Pumps Interactive
Carnot Engine The most efficient heat engine possible is the Carnot engine –A theoretical heat engine operating in an ideal, reversible cycle (a cycle in which system can be returned to its initial state along the same path) called the Carnot cycle –Note that a truly reversible process is an idealization, and real processes are irreversible (although some are close to being reversible) PV diagram of the cycle: –Consists of 2 adiabatic and 2 isothermal processes, all reversible –Net work done W is net energy received in one cycle: W = Q h – Q c
Carnot Cycle Assume the substance that changes temperature is an ideal gas Gas is contained in cylinder with movable piston at one end Steps of the cycle: –A B: Gas expands isothermally while in contact with reservoir at T h –B C: Gas expands adiabatically (Q = 0) –C D: Gas compressed isothermally while in contact with reservoir at T c < T h –D A: Gas compressed adiabatically –Note that upward (downward) red arrows on piston indicate removal (addition) of sand
Carnot Engine Carnot showed that the efficiency of the engine depends on the temperatures of the reservoirs: –Temperatures must be in Kelvin –All Carnot engines operating between the same two temperatures will have the same efficiency –The efficiency increases as T c is lowered and as T h is raised –Efficiency is 0 if T h = T c –Efficiency is 100% only if T c = 0 K (not possible from third law of thermodynamics) –In most practical cases T c is near room temperature (300 K) so generally T h is raised to increase efficiency –All real engines are less efficient than the Carnot engine (friction, cycle completed in brief time period)
Example Problem #12.27 Solution (details given in class): (a)0.672 (or 67.2%) (b)58.8 kW One of the most efficient engines ever built is a coal- fired steam turbine engine in the Ohio River valley, driving an electric generator as it operates between 1870°C and 430°C. (a)What is its maximum theoretical efficiency? (b)Its actual efficiency is 42.0%. How much mechanical power does the engine deliver if it absorbs J of energy each second from the hot reservoir?