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Physics 103: Lecture 21 Thermal Physics

Physics 103: Lecture 21 Thermal Physics. Specific Heat Phase Changes Latent Heat. To Change Temperature…. Add internal energy to system Heat … a form of energy Q = c m T Q = amount of heat that must be supplied to raise the temperature of mass m by an amount T

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Physics 103: Lecture 21 Thermal Physics

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  1. Physics 103: Lecture 21Thermal Physics • Specific Heat • Phase Changes • Latent Heat Physics 103, Fall 2009, U. Wisconsin

  2. To Change Temperature…. • Add internal energy to system • Heat … a form of energy • Q = c m T • Q = amount of heat that must be supplied to raise the temperature of mass m by an amount T • [Q] = Joules or calories • 1 cal = 4.186 J • 1 kcal = 1 Cal = 4186 J • Specific heat, c • amount of heat that must be supplied to raise T of 1 kg by 1C • [c] = J/(kg-C) • “Cause” = “inertia” x “effect” (just like F=ma) • cause = Q • effect = T • inertia = c m Physics 103, Fall 2009, U. Wisconsin

  3. Specific Heat • Adding heat energy (Q) to a substance increases its temperature (DT) • The magnitude of change in temperature (DT) depends on the amount (m) and the type (specific heat - c) of that substance The specific heat of substance A is greater than that of substance B. If equal amount of heat energy is added to equal masses of these two substances initially at the same temperature, which one reaches higher final temperature? Solve the equation for T substance B. Provided there is no change in the phase of substances(next subject) Physics 103, Fall 2009, U. Wisconsin

  4. lead Specific Heat You have various types of materials at the same initial temperature. You add 1000J of heat to each of them of them. Which one ends up at the higher final temperature Substance c in J/(kg-C) aluminum 900 copper 387 iron 452 lead 128 human body 3500 water 4186 ice 2000 Lead is used as solder which is designed to be easy to melt. The answer is consistent with our knowledge. Physics 103, Fall 2009, U. Wisconsin

  5. Consequences of Differing Specific Heats • Water has a high specific heat compared to land • On a hot day, the air above the land warms faster • The warmer air flows upward and cooler air moves toward the beach Physics 103, Fall 2009, U. Wisconsin

  6. Calorimetry • Conservation of energy applies to the whole system • Consider piece of hot metal placed in cooler water • The energy that leaves the warmer substance equals the energy that enters the water • Qcold = -Qhot • Negative sign keeps consistency in the sign convention of ∆T • In some cases with more than two materials, it may be difficult to determine which materials gain heat and which materials lose heat • You can start with SQ = 0, For two substances Qcold + -Qhot … = 0 • Each Q = m c DT • and DT = Tf – Ti • You don’t have to determine before using the equation which materials will gain or lose heat Physics 103, Fall 2009, U. Wisconsin

  7. Problem 1 Suppose you have an insulated bucket containing 2 kg water at T=25C. You also have a block of aluminum of mass 4 kg at T=75C. You put the aluminum block in the bucket. What is the final temperature of the water? Answer: 40C Suppose you three substances Physics 103, Fall 2009, U. Wisconsin

  8. Phase Changes • Solid - Liquid • Liquid - Gas Physics 103, Fall 2009, U. Wisconsin

  9. correct Boiling Water You begin to observe water in a beaker beginning to boil on a hot plate. As you add more heat to the water which is still boiling, its temperature • Increases • Stays constant • Decreases Physics 103, Fall 2009, U. Wisconsin

  10. T TS rises TW rises Water changes to steam Q added to water Latent Heat Latent Heat L [J/kg]: amount of heat per kg needed to add to or remove from a substance to change the state of that substance Q=mLf (melting-freezing) Q=mLv (vaporization-condensation) Substance Lf (J/kg) Lv (J/kg) water 33.4 x 104 22.56 x 105 Physics 103, Fall 2009, U. Wisconsin

  11. Graph of Ice to Steam Physics 103, Fall 2009, U. Wisconsin

  12. Warming Ice • Start with one gram of ice at –30.0º C • During A, the temperature of the ice changes from –30.0º C to 0º C • Use Q = m c DT Physics 103, Fall 2009, U. Wisconsin

  13. Melting Ice • Once at 0º C, the phase change (melting) starts • The temperature stays the same although energy is still being added • Use Q = m Lf Physics 103, Fall 2009, U. Wisconsin

  14. Warming Water • Between 0º C and 100º C, the material is liquid and no phase changes take place • Energy added increases the temperature • Use Q = m c DT • c is different for water than ice! Physics 103, Fall 2009, U. Wisconsin

  15. Boiling Water • At 100º C, a phase change occurs (boiling) • Temperature does not change • Use Q = m Lv Physics 103, Fall 2009, U. Wisconsin

  16. Heating Steam • After all the water is converted to steam, the steam will heat up • No phase change occurs • The added energy goes to increasing the temperature • Use Q = m c DT • However it’s now a gas and it will expand or go up in pressure depending on the situation. Physics 103, Fall 2009, U. Wisconsin

  17. Summer in Arizona Summers in Phoenix Arizona are very hot (125 F is not uncommon), and very dry. If you hop into an outdoor swimming pool on a summer day in Phoenix, you will probably find that the water is too warm to be very refreshing. However, when you get out of the pool and let the sun dry you off, you find that you are quite cold for a few minutes (yes...you will have goose-bumps on a day when the air temperature is over 120 degrees). How can you explain this? As the water evaporates off of you, it takes a great deal of heat from your body to gain the energy needed to evaporate... this makes you cold. Physics 103, Fall 2009, U. Wisconsin

  18. Next Time: Phase Changes • Ideal Gas at Constant Temperature: PV = Constant • Deviation at Critical Temperature - phase change - transition to liquid phase • Critical Pressure – minimum for which liquid to exists at TC Physics 103, Fall 2009, U. Wisconsin

  19. Equilibrium • Liquid and Gas phases are in equilibrium at the boiling temperature. • For water and steam that point is (P=1 atm, T=100oC) • If both temperature and pressure are raised, the equilibrium can be maintained. Physics 103, Fall 2009, U. Wisconsin

  20. Phase Changes • Not really a ideal gas or a liquid above the critical temp, Tc. A supercritical fluid • Critical point: At Tc and the critical pressure • Liquid to the left (small V large P) of the critical point below Tc • Ideal gas to the right (large V small P) of the critical point below Tc • Liquid or gas below the critical point - phase change region • If P high enough can make a solid Physics 103, Spring 2007, U. Wisconsin

  21. Phase Changes • Ideal Gas at Constant Temperature: PV = Constant • Deviation at Critical Temperature - phase change - transition to liquid phase • Critical Pressure - minimum needed for liquid to exist at TC Physics 103, Fall 2009, U. Wisconsin

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

  23. Air water p “Phase Diagram” 1 atm .5 atm T 83C 100C Phase changes • Liquid-vapor equilibrium reached • Boiling occurs when pvap  partial pressure of the water in the air • Boiling water on mountain • boils at T<100C • Boiling water in pressure cooker • boils at T>100C Physics 103, Fall 2009, U. Wisconsin

  24. H2O • Triple Point and Critical Point • Triple point provides much more accurate calibration than freezing and boiling points • The freezing and boiling points depend on pressure Physics 103, Fall 2009, U. Wisconsin

  25. Vapor Pressure and Partial Pressure • Dalton’s Law : The total pressure is the sum of partial pressures of the component gases, assuming ideal gas behavior and no chemical reactions. • Vapor pressure is the gas pressure created by the liquid and solid phases of a substance. • Water evaporates and ice sublimates when their vapor pressures exceed the partial pressure of water in the surrounding mixture of gases (air). • If the vapor pressure is less than the partial pressure of water vapor in the surrounding air, then condensation or frost forms. Physics 103, Fall 2009, U. Wisconsin

  26. Problem 2 A large punch bowl holds 4 kg of water at 20C. A 0.5-kg ice cube at 0C is placed in the water. What is the final temperature of the system? Answer: all the ice melts; ~8.9C Physics 103, Fall 2009, U. Wisconsin

  27. correct Lecture 20,Preflight 1 & 2 Suppose you have two insulated buckets containing the same amount of water at room temperature. You also happen to have two blocks of metal of the same mass, both at the same temperature, warmer than the water in the buckets. One block is made of aluminum and one is made of copper. You put the aluminum block into one bucket of water, and the copper block into the other. After waiting a while you measure the temperature of the water in both buckets. Which is warmer? 1. The water in the bucket containing the aluminum block 2. The water in the bucket containing the copper block 3. The water in both buckets will be at the same temperature Substance c in J/(kg-C) aluminum 900 copper 387 • Q = [c m] T • Q = heat given up by the metal • Copper has smaller “inertia” • Therefore, the water has a larger “effect” on the copper • effect is drop in temperature • Copper temperature drops more than aluminum • Thus, water in the bucket with aluminum block ends up with higher final temperature Physics 103, Fall 2009, U. Wisconsin

  28. Lecture 20 : Preflight 4 An open 10 ml container filled to the brim with water is left on the counter in a room held at constant 20oC at atmospheric pressure. After a few days, it is observed that the water has completely disappeared. What happens if the container were sealed tightly with very little air enclosed in it? 1. Water in it will still evaporate in the same number of days 2. Water in it will still evaporate but will take much longer time 3. Water in it will still evaporate but will take much shorter time 4. Water in it will not evaporate Water evaporated when placed in the open container at a temperature much lower than the boiling point because it was surrounded by air rather than solely by water vapor. In a sealed container the water does not evaporate because the small sealed volume will have sufficient vapor in equilibrium with liquid water. Physics 103, Fall 2009, U. Wisconsin

  29. correct Lecture 20,Preflight 3 Which of the following statements is true? 1. Energy is released in the process of melting 2. Energy is released in the process of evaporation 3. Energy is released in the process of condensation Q=mLv Energy is needed to vaporize. Energy is released in the reverse condensation process. Physics 103, Fall 2009, U. Wisconsin

  30. Lecture 19(20), Preflight 8(5) In a sealed pressure cooker water boils at:     1. lower temperature than in an open container 2. the same temperature as in an open container 3. higher temperature than in an open container • Liquid and Gas phases are in equilibrium at the boiling temperature. • For water and steam that point is (P=1 atm, T=100oC) • If both temperature and pressure are raised, the equilibrium can be maintained. • Since pressure is higher the boiling point is higher in the sealed container. • Food gets cooked faster • In contrast, cooking takes much longer at high altitude as the water boils off at lower temperature. Physics 103, Fall 2009, U. Wisconsin

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