Page 1Physics 207 – Lecture 24Physics 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 2(4) Isobaric(3) Isothermal (2) Isochoric(1) Adiabatic Paths on the pV diagrampV2134T1T2T3T4W = - p ∆V????W = 0???? IdealgasPage 2Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 3Isothermal processes Work done when PV = nRT = constant P = nRT / V∫−=−=finalinitial)curveunder area( dVpW∫∫−=−=fifiVVVV/ nRT/ nRT VdVVdVW)/VV( nRTifnWl−=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 casePVγ= const. All real processes are not.pV2134T1T2T3T4Page 3Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 5Work and Ideal Gas Processes (on system) Isothermal)/VV( nRTifnWl−= Isobaric)V-V( pif−=W Isochoric0=W)(12constconst2121γγγγ−−−=−=−=∫∫VVPdVWVVVVVdVV FYI: 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!Page 4Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 7Relationship between energy transfer and TPhysics 207: Lecture 24, Pg 8Heat and Latent Heat Latent heat of transformation L is the energy required for 1 kg of substance to undergo a phase change. (J / kg)Q = ±ML Specific 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 T Molar 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 CVTIf a phase transition involved then the heat transferred is Q = ±ML+M c TPage 5Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 9Q : Latent heat and specific heat The molar specific heat of gasses depends on the process path CV= molar specific heat at constant volume Cp= molar specific heat at constant pressure Cp= CV+R (R is the universal gas constant)VCCp=γPhysics 207: Lecture 24, Pg 10Mechanical equivalent of heat Heating 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 lostPage 6Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 11Exercise The specific heat (Q = M c T) 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−=+==∆ 0Th Isobaric IsochoricTnCQV∆=TRCnTnCQVp∆+=∆=)( Adiabatic 0=QPage 7Physics 207 – Lecture 24Physics 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 byprocess B.A. WA> WBB. WA< WBC. WA= WB= 0D. WA= WBbut neither is zeroON BYA 1 3 W1 2= 0 (isochoric)B 1 2 W1 2= -½ (p1+p2)(V2-V1) < 0 -W1 2> 0B 2 3 W2 3= -½ (p2+p3)(V1-V2) > 0 -W2 3< 0B 1 3 = ½ (p3 - p1)(V2-V1) > 0 < 0Physics 207: Lecture 24, Pg 14 Most 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 latentheat 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 HeatPage 8Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 15Energy transfer mechanisms Thermal conduction (or conduction) Convection Thermal RadiationFor a material of cross-section area A and length L, spanning a temperature difference T = 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 mechanisms Thermal 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, Tcand ThQ / ∆t = k A (Th- Tc) / ∆x k :Thermal conductivity (J / s m °C)Page 9Physics 207 – Lecture 24Physics 207: Lecture 24, Pg 17Thermal Conductivities0.10Wood0.2Rubber427Silver0.60Water0.0238Oxygen34.7Lead1.6Ice0.0234Nitrogen79.5Iron0.84Glass0.172Hydrogen314Gold1.3Concrete0.138Helium397Copper0.25Asbestos0.0234Air238AluminumJ/s m °CJ/s m °CJ/s m °CPhysics 207: Lecture
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