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phys213 Lecture 6

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1Lecture 6: 1/25/06• Homework HW#1 due before class.  HW#2 due next Wednesday before class. Problem at end of lecture. MP#6 is due Friday at 1pm. No new reading (Should be through 20.7 by now)• Practice problems from Serway (Not to be turned in!) Problems 20-28, 20-30, 20-32, 20-34 (solution posted outside EPS106)• Assessment key and tallies of answers per question posted on bulletin board• Lab  Lab next week: Mechanical Equivalent of Heat • Topics to cover today Review Specific Heat and Latent Heat First law of Thermodynamics• PV diagrams• ApplicationsReview of Specific and Latent Heat• Specific Heat, c , is the Heat Capacity per unit mass c is in J/(kg °C)• The energy transferred by heat or work to raise object by ∆T ∆Ein= Q or W = C ∆T = m c ∆T•∆T = Tf-Ti• Latent Heat of Fusion, Lf Energy per unit mass to go from solid to liquid (at melting point) Total energy transferred for a mass, m, solid<->liquid• Q = ±m Lf• Latent Heat of Vaporization, Lv Energy per kg to go from liquid to gas (at boiling point) Total energy transferred for a mass, m, liquid <-> gas• Q = ±m LvWork Done on a Gas• Quasi-Static Expansion (stays in thermal equilibrium)• Very small change in volume  Pressure constanthAh-dhAPV Diagram• Work on system depends on pathPfPiVfViifPfPiVfViifPfPiVfViif• Work on system is negative the "area under path"• Work is not a function of temperature (and n) Though temperature effects P & VfiVVWPdV=−∫Energy Transferred by Heat to a Gas• Thermally insulated sides and top• Base is kept at Tiwhile piston is slowly withdrawn Thermal equilibrium => Gas is kept at Ti• Pressure of gas pushes piston upTiTiTiTf= TiEnergy Transferred by Heat to a Gas• Thermally insulated container with thin membrane Initial volume, pressure, and temperature• The same as previous example Initial• Very thin membrane is popped No work done No energy transferred by heatTiTf= TiThinMembraneVacuum2First Law of Thermodynamics• Work done on system depends on path, W• Heat transferred into system depends on path, Q• The internal energy of a state of a system  Is independent of path it takes to get to that state For a gas system (with constant n)• Internal energy is a function of P and V, independent of path• 1st Law During a process (change from initial to final state along any path)•∆Ein= Q + W• Types of thermodynamic processes Adiabatic: Q = 0 Adiabatic Free Expansion: Q = 0 and W = 0 Isobaric: Constant Pressure Isovolumetric: Constant Volume Isothermal: Constant TemperatureHW#2: Free Merri and Bill's Boat!• See homework guidelines from 1/18/06 lecture.• DEFINE VARIABLES AND DERIVE ALGEBRAIC EXPRESSIONS BEFORE PLUGGING IN NUMBERS • Before winter hit, Merri and Bill pulled their flat bottomed boat (7.0 meters long by 2.0 meters wide) out of the river and into a protected flat hollow (8.0 meters by 3.0 meters). But, then rain flooded the hollow and it got really cold, so the boat was frozen solid in ice. It stayed frozen all winter. For the entire month of March, the temperature was -20°C both day and night. On March 25, they developed a plan to free the boat. They measured the ice thickness to be 12 cm thick throughout the hollow. Their plan was to heat up huge rocks (20 kg each) in the fire to 250°C and place the rocks on the ice around the boat and then use blankets and leaves to insulate the hollow while the rocks melted the ice.• What is the minimum number of rocks Merri and Bill must use to completelymelt all the ice in the hollow and free their boat? • Give answer in terms of known variables. Then plug in numbers and get answer.• State ALL your assumptions that you used, consistent with the problem and your answer. Assume the boat is open to the air, has a thin bottom, and has a draw of 23 cm. Different assumptions may lead to different answers, which is fine. As long as your answer matches your assumptions, it is a correct answer.• Possibly helpful information.  For the specific heat of rock, use 920 J/(kg-°C) Density of ice = 0.92 gm/ cm3 Use tables in Serway for other values

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