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Physics 103: Lecture 23

Review Heat Transfer Heat and Work The Laws of Thermodynamics. Physics 103: Lecture 23. L. T H Hot. T C Cold. Area A. Heat Transfer: Conduction. Hot molecules have more KE than cold molecules High-speed molecules on right collide with low-speed molecules on left

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Physics 103: Lecture 23

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  1. Review Heat Transfer Heat and Work The Laws of Thermodynamics Physics 103: Lecture 23 Physics 103, Fall 2009, U.Wisconsin

  2. L TH Hot TC Cold Area A Heat Transfer: Conduction • Hot molecules have more KE than cold molecules • High-speed molecules on right collide with low-speed molecules on left • “billiard ball” type collisions • Net result: • energy to lower-speed molecules • heat transfers from hot to cold • Rate of heat transfer (power) [J/s] = Q/t • P=Q/t = k A (TH-TC)/L • Q/t = k A T/ x • k = “thermal conductivity” • [k] = J/s-m-C • good thermal conductors…high k • good thermal insulators … low k • what about vacuum? Caution: ‘k’ is used sometimes to denote Boltzman constant - figure out from context! Physics 103, Fall 2009, U.Wisconsin

  3. heater Heat Transfer: Convection • Air heats at bottom • Thermal expansion…density reduces • Lower density air rises • Archimedes: low density floats on high density • Cooler air pushed down • Cycle continues; Net result : Air circulation • Practical aspects • heater ducts on floor • A/C ducts on ceiling • stove heats water from bottom • “riding the thermals birds/hangliders” Physics 103, Fall 2009, U.Wisconsin

  4. Heat Transfer: Radiation • All things radiate electromagnetic energy • Pemit = Q/t = eAT4 (in Watts) • e = emissivity (between 0 and 1) • T is Kelvin temperature •  = Stefan-Boltzmann constant = 5.67 x 10-8 J/s-m2-K4 • No “medium” required • All things absorb energy from surroundings • Pabsorb = eAT04 • perfect absorber (“black body”) has e=1 • Ideal reflector absorbs no energy incident on it: e=0 • good absorbers (e close to 1) are also good emitters • Net rate of heat transfer by radiation from a body at temperature T, if the surrounding temperature is T0 • Q/t = s e A (T4-T04) • Examples • hot stove in room • Heat from the sun • Starlight Physics 103, Fall 2009, U.Wisconsin

  5. Work in Thermodynamic Processes • Noted before that PV has units of N-m, J, Work or Energy • We can do work to change the state of a system - changing P, V or T • Work is an important energy transfer mechanism in thermodynamic systems - along with heat • State of a system • Description of the system in terms of state variables • Pressure • Volume • Temperature • A macroscopic state of a system can be specified only if the system is in internal thermal equilibrium Physics 103, Fall 2009, U.Wisconsin

  6. Work in a Gas Cylinder • The gas is contained in a cylinder with a moveable piston • The gas occupies a volume V and exerts pressure P on the walls of the cylinder and on the piston Physics 103, Fall 2009, U.Wisconsin

  7. Work in a Gas Cylinder, cont. • A force is applied to slowly compress the gas • The compression is slow enough for all the system to remain essentially in thermal equilibrium • W = - P DV • This is the work done on the gas • If the pressure remains constant during the compression or expansion • This is called an isobaric process • If the pressure changes, the average pressure may be used to estimate the work done Physics 103, Fall 2009, U.Wisconsin

  8. More about Work on a Gas Cylinder • When the gas is compressed • DV is negative • The work done on the gas is positive • When the gas is allowed to expand • DV is positive • The work done on the gas is negative • When the volume remains constant • No work is done on the gas Physics 103, Fall 2009, U.Wisconsin

  9. PV Diagrams • Used when the pressure and volume are known at each step of the process • The magnitude of the work done on a gas that takes it from some initial state to some final state is the area under the curve on the PV diagram • This is true whether or not the pressure stays constant • Find the sign from whether the volume increases or decreases Physics 103, Fall 2009, U.Wisconsin

  10. Thermodynamic Processes • Isobaric • Pressure stays constant • Horizontal line in PV diagram • Isovolumetric • Volume stays constant • Vertical line on the PV diagram • Isothermal • Temperature stays the same (PV = constant) • Hyperbola in PV diagram • Adiabatic • No heat is exchanged with the surroundings Physics 103, Fall 2009, U.Wisconsin

  11. First Law of Thermodynamics • Quantities of interest • Q - Heat • Positive if energy is transferred to the system • W - Work • Positive if done on the system • U - Internal energy • Positive if the temperature increases • The relationship among U, W, and Q can be expressed as • DU = Uf – Ui = Q + W • This means that the change in internal energy of a system is equal to the sum of the energy transferred across the system boundary by heat and the energy transferred by work Physics 103, Fall 2009, U.Wisconsin

  12. P(atm) P(atm) A B 4 4 A B 2 2 Case 1 Case 2 correct 3 9 3 9 V(m3) V(m3) Preflight 2 Shown in the picture below are the pressure versus volume graphs for two thermal processes, in each case moving a system from state A to state B along the straight line shown. In which case is the change in internal energy of the system the biggest? 1. Case 1 2. Case 2 3. Same P1AV1A=2x3=6, P1BV1B=4x9=36, 6 to 36 P2AV2A=4x3=12, P2BV2B=2x9=18, 12 to 18 PV or T tell us about the internal energy U T increase higher in case 1 than in case 2 Therefore, U increases more in case 1 than in case 2 Physics 103, Fall 2009, U.Wisconsin

  13. P(atm) P(atm) A B 4 4 A B 2 2 Case 1 Case 2 correct 3 9 3 9 V(m3) V(m3) Follow up Question Shown in the picture below are the pressure versus volume graphs for two thermal processes, in each case moving a system from state A to state B along the straight line shown. In which case is the heat added to the system the biggest? 1. Case 1 2. Case 2 3. Same Q1 = DU1 - W Q2 = DU2 - W W is the same for both, but DU1 > DU2 Physics 103, Fall 2009, U.Wisconsin

  14. Additional Notes About the First Law • The First Law is a general equation of Conservation of Energy • There is no practical, macroscopic, distinction between the results of energy transfer by heat and by work • Q and W are related to the properties of state for a system Physics 103, Fall 2009, U.Wisconsin

  15. Thermodynamic Processes: Cyclic • Isovolumetric • Volume stays constant • Vertical line on the PV diagram • +Q, Heat added • Isothermal • Temperature stays the same (PV = constant) • Hyperbola in PV diagram • Neg W, work done, on outside world, -W=Q • Isobaric • Pressure stays constant • Horizontal line in PV diagram • +W, Work done on system and -Q, Heat removed • WBC > WCA, More work done on the outside world, heat added to do this work • DU = 0 • Don’t forget adiabatic - no heat transferred Physics 103, Spring 2008, U. Wisconsin

  16. Applications of the First Law – Isovolumetric Process • No change in volume, therefore no work is done • The energy added to the system goes into increasing the internal energy of the system • Temperature will increase • Sometimes called “Isochoric” Physics 103, Spring 2008, U. Wisconsin

  17. Applications of the First Law –Isothermal Processes • Isothermal means constant temperature • The cylinder and gas are in thermal contact with a large source of energy • Allow the energy to transfer into the gas (by heat) • The gas expands and pressure falls to maintain a constant temperature • The work done is the negative of the heat added • Work is done on the outside world, spinning a car’s tires Physics 103, Spring 2008, U. Wisconsin

  18. Applications of the First Law – Isobaric Process • No change pressure. Work can be done proportional to the change in volume • If the volume increases work is done by the system: neg W • If the volume decreases work is on the system: pos W • Second case, pos W: The energy added to the system normally goes into increasing the internal energy of the system • Temperature will increase: PV = NkBT • If the volume decreases and the pressure stays the same the system must lose heat, neg Q Physics 103, Spring 2008, U. Wisconsin

  19. Applications of the First Law – Adiabatic Process • Energy transferred by heat is zero • The work done is equal to the change in the internal energy of the system • One way to accomplish a process with no heat exchange is to have it happen very quickly. Another way is to keep the system isolated. • In an adiabatic expansion, the work done is negative and the internal energy decreases • These processes will be important in the carnot cycle Physics 103, Spring 2008, U. Wisconsin

  20. Heat Engine, cont. • Since it is a cyclical process, DU = 0 • Its initial and final internal energies are the same • Therefore, Qnet = Weng • The work done by the engine equals the net energy absorbed by the engine • The work is equal to the area enclosed by the curve of the PV diagram Physics 103, Spring 2008, U. Wisconsin

  21. Extra Physics 103, Fall 2009, U.Wisconsin

  22. Asphalt and Cement One day during the winter, the sun has been shining all day. Toward sunset a light snow begins to fall. It collects without melting on a cement playground, but it melts immediately upon contact on a black asphalt road adjacent to the playground. How do you explain this? Frictional heat generated when snow falls on rough asphalt road melts the snow Black asphalt road radiates more heat; snow only melts on cement roads which are lighter in color - observation is stated incorrectly. Black asphalt road absorbs more heat; thus, it is hotter and the snow will melt more readily. Physics 103, Fall 2009, U.Wisconsin

  23. Heat Transfer • Conduction: Though collisions between molecules • Q/t = k A T/ x • R = x/k , R = R1+R2+R3… • Convection: Though movement of the air or liquid • Radiation: All things radiate electromagnetic energy • Pemit = Q/t = eAT4 (in Watts) • e = emissivity (between 0 and 1) • perfect absorber (“black body”) has e=1 • Ideal reflector absorbs no energy incident on it: e=0 • T is Kelvin temperature •  = Stefan-Boltzmann constant = 5.67 x 10-8 J/s-m2-K4 • No “medium” required • All things absorb energy from surroundings • Pabsorb = eAT04 • good emitters (e close to 1) are also good absorbers • Net rate of heat transfer by radiation from a body at temperature T, if the surrounding temperature is T0 • Q/t = s e A (T4-T04) Physics 103, Fall 2009, U.Wisconsin

  24. Example: Lava cooling Lava beds and slag heaps cool very slowly. Calculate the rate of heat conduction per square meter through a 30 m thickness of granite if the surface temperature is 20oC and interior is 50oC. At this rate, how long does it take for enough heat to flow to cool 1 m3 (2700 kg) of granite by 1oC? Physics 103, Fall 2009, U.Wisconsin

  25. 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 • The metabolic rate (DU / Dt) is directly proportional to the rate of oxygen consumption by volume • Metabolic rate (to maintain and run organs, etc.) is about 80 W Physics 103, Fall 2009, U.Wisconsin

  26. Various Metabolic Rates Physics 103, Fall 2009, U.Wisconsin

  27. Aerobic Fitness • One way to measure a person’s physical fitness is their maximum capacity to use or consume oxygen Physics 103, Fall 2009, U.Wisconsin

  28. Efficiency of the Human Body • Efficiency is the ratio of the mechanical power supplied to the metabolic rate or total power input Physics 103, Fall 2009, U.Wisconsin

  29. Applications of the First Law –Isolated System • An isolated system does not interact with its surroundings • No energy transfer takes place and no work is done • Therefore, the internal energy of the isolated system remains constant Physics 103, Fall 2009, U.Wisconsin

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