Lecture 24Isothermal processesAdiabatic ProcessesWork and Ideal Gas Processes (on system)Combinations of Isothermal & Adiabatic ProcessesRelationship between energy transfer and THeat and Latent HeatQ : Latent heat and specific heatMechanical equivalent of heatExerciseHeat and Ideal Gas Processes (on system)Slide 13Exercise Latent HeatEnergy transfer mechanismsSlide 16Thermal ConductivitiesExercise Thermal ConductionSlide 21Minimizing Energy TransferAnti-global warming or the nuclear winter scenarioCh. 18, Macro-micro connection Molecular Speeds and CollisionsMolecular Speeds and CollisionsSlide 26Mean Free PathMacro-micro connectionSlide 29Physics 207: Lecture 24, Pg 1Lecture 24Goals:Goals:•Chapter 17Chapter 17 Apply heat and energy transfer processes Recognize adiabatic processes•Chapter 18Chapter 18 Follow the connection between temperature, thermal energy, and the average translational kinetic energy molecules Understand the molecular basis for pressure and the ideal-gas law. To predict the molar specific heats of gases and solids.•AssignmentAssignment HW10, Due Wednesday 9:00 AM For Thursday, Read through all of Chapter 18Physics 207: Lecture 24, Pg 3Isothermal processesWork done when PV = nRT = constant P = nRT / Vfinalinitial)curveunder area( dVpWfifiVVVV/ nRT/ nRT VdVVdVW)/VV( nRTifnW pV3T1T2T3T4Physics 207: Lecture 24, Pg 4Adiabatic Processes An adiabatic process is process in which there is no thermal energy transfer to or from a system (Q = 0) A reversible adiabatic process involves a “worked” expansion in which we can return all of the energy transferred.In this casePV = const.All real processes are not.pV2134T1T2T3T4Physics 207: Lecture 24, Pg 5Work and Ideal Gas Processes (on system)Isothermal)/VV( nRTifnW Isobaric)V-V( pifWIsochoric0W)(12constconst2121VVPdVWVVVVVd VVFYI: Adiabatic (and reversible)Physics 207: Lecture 24, Pg 6Combinations of Isothermal & Adiabatic ProcessesAll engines employ a thermodynamic cycleW = ± (area under each pV curve)Wcycle = area shaded in turquoiseWatch sign of the work!Physics 207: Lecture 24, Pg 7Relationship between energy transfer and TPhysics 207: Lecture 24, Pg 8Heat and Latent HeatLatent heat of transformation L is the energy required for 1 kg of substance to undergo a phase change. (J / kg)Q = ±MLSpecific heat c of a substance is the energy required to raise the temperature of 1 kg by 1 K. (Units: J / K kg )Q = M c ΔTMolar specific heat C of a gas at constant volume is the energy required to raise the temperature of 1 mol by 1 K.Q = n CV ΔTIf a phase transition involved then the heat transferred is Q = ±ML+M c ΔTPhysics 207: Lecture 24, Pg 9Q : Latent heat and specific heatThe molar specific heat of gasses depends on the process pathCV= molar specific heat at constant volumeCp= molar specific heat at constant pressureCp= CV+R (R is the universal gas constant)VCCpPhysics 207: Lecture 24, Pg 10Mechanical equivalent of heatHeating liquid water: Q = amount of heat that must be supplied to raise the temperature by an amount T . [Q] = Joules or calories. calorie: energy to raise 1 g of water from 14.5 to 15.5 °C(James Prescott Joule found the mechanical equivalent of heat.) 1 Cal = 4.186 J1 kcal = 1 Cal = 4186 JSign convention:+Q : heat gained- Q : heat lostPhysics 207: Lecture 24, Pg 11ExerciseThe specific heat (Q = M c ΔT) of aluminum is about twice that of iron. Consider two blocks of equal mass, one made of aluminum and the other one made of iron, initially in thermal equilibrium.Heat is added to each block at the same constant rate until it reaches a temperature of 500 K. Which of the following statements is true? (a) The iron takes less time than the aluminum to reach 500 K (b) The aluminum takes less time than the iron to reach 500 K (c) The two blocks take the same amount of time to reach 500 KPhysics 207: Lecture 24, Pg 12Heat and Ideal Gas Processes (on system)Isothermal Expansion/ContractionWQQWE 0ThIsobaricIsochoricTnCQVTRCnTnCQVp )(Adiabatic 0QPhysics 207: Lecture 24, Pg 13Two process are shown that take an ideal gas from state 1 to state 3. Compare the work done by process A to the work done by process B.A. WA > WBB. WA < WB C. WA = WB = 0D. WA = WB but neither is zeroON BYA 1 3 W12 = 0 (isochoric)B 1 2 W12 = -½ (p1+p2)(V2-V1) < 0 -W12 > 0B 2 3 W23 = -½ (p2+p3)(V1-V2) > 0 -W23 < 0B 1 3 = ½ (p3 - p1)(V2-V1) > 0 < 0Physics 207: Lecture 24, Pg 14Most people were at least once burned by hot water or steam. Assume that water and steam, initially at 100°C, are cooled down to skin temperature, 37°C, when they come in contact with your skin. Assume that the steam condenses extremely fast, and that the specific heat c = 4190 J/ kg K is constant for both liquid water and steam.Under these conditions, which of the following statements is true?(a) Steam burns the skin worse than hot water because the thermal conductivity of steam is much higher than that of liquid water.(b) Steam burns the skin worse than hot water because the latent heat of vaporization is released as well.(c) Hot water burns the skin worse than steam because the thermal conductivity of hot water is much higher than that of steam.(d) Hot water and steam both burn skin about equally badly.Exercise Latent HeatPhysics 207: Lecture 24, Pg 15Energy transfer mechanismsThermal conduction (or conduction)ConvectionThermal RadiationFor a material of cross-section area A and length L, spanning a temperature difference ΔT = TH – TC, the rate of heat transfer iswhere k is the thermal conductivity, which characterizes whether the material is a good conductor of heat or a poor conductor.Q / t = k A T / xPhysics 207: Lecture 24, Pg 16Energy transfer mechanismsThermal conduction (or conduction): Energy transferred by direct contact. e.g.: energy enters the water through the bottom of the pan by thermal conduction. Important: home insulation, etc. Rate of energy transfer ( J / s or W ) Through a slab of area A and thickness x, with opposite faces at different temperatures, Tc and Th Q / t = k A (Th - Tc ) / x k
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