12.8 Heat and Phase Change: Latent Heat

1. 12.8 Heat and Phase Change: Latent Heat • Glass of ice water at 0 C. Heat is being used to melt ice, and then only when all the ice is melted will the temperature of the liquid begin to rise.

2. Heat and Phase Change: Latent Heat • A solid can melt or fuse into a liquid if heat is added. • Liquid can freeze into a solid if heat is removed. • A liquid can evaporate into a gas if heat is supplied. • Gas can condense into a liquid if heat is taken away. • Rapid evaporation, formation of vapor bubbles within the liquid is called boiling. • A solid can change directly into a gas if that is provided, called sublimation.

3. Example: dry ice (CO2) • Solid naphthalene (moth balls) turns into naphthalene fumes. • http://www.youtube.com/watch?v=cTP4yp8y_NA

5. Conceptual Example 13: Saving Energy Suppose you are cooking spaghetti for dinner, and the instructions say “boil the pasta in water for ten minutes.” To cook spaghetti in an open pot with the least amount of energy, should you turn up the burner to its fullest so the water vigorously boils, or should you turn down the burner so the water barely boils?

6. Latent Heat • Heat needed for a phase change. • A substance changes from one phase to another, the amount of heat that must be added or removed depends on the type of material and the nature of the phase change. The heat Q that must be supplied or removed to change the phase of a mass m of a substance is. Q = mL Where L is the latent heat of the substance. SI Unit of Latent Heat: j/kg

7. Latent Heat • Latent heat of fusion: Lf, refers to the change between solid and liquid phases. • Latent heat of vaporization Lv, change between liquid and gas phases. • Latent heat of sublimation Ls: change between solid and gas phases. • Lf = 3.35 x 10^5 J/kg water • So 3.35 x 10^5 J/kg of heat must be supplied to melt one kilogram of ice at 0 C. • This amt. of heat must be removed from one kilogram of liquid water at 0 C to freeze the liquid into ice.

8. Latent heat of vaporization for water has the much larger value of Lv = 22.6 x 10^5 J/kg • When water boils at 100 C, 22.6 x 10^5 J of heat must be supplied for each kilogram of liquid turned into steam. • When steam condenses at 100 C, this amt. of heat is released from each kilogram of steam that changes back into liquid.

9. In the Real World • Designers can engineer clothing that can absorb or release heat to help maintain a comfortable and constant temperature close to your body. • PCM “phase change material” • Prevents overheating by melting, absorbing excess body heat in the process. • PCM freezes and releases heat to keep you warm. http://www.newlaunches.com/archives/nike_precool_vest.php

11. Example 14: Ice-Cold Lemonade Ice at 0 C is placed in a styrofoam cup containing 0.32 kg of lemonade at 27 C. The specific heat capacity of lemonade is virtually the same as that of water; that is, c = 4186 J/(kgxC). After the ice and lmonade reach an equilibrium temperature, some ice still remains. The latent heat of fusion for water is Lf = 3.35 x 10^5 J/kg. Assume that the mass of the cup is so small that it absorbs a negligible amount of heat, and ignore any heat lost to the surroundings. Determine the mass of ice that has melted.

14. Example 15: Getting Ready for a Party A 7.00kg glass bowl (c = 840 J/(kgxC)) contains 16.0kg of punch at 25 C. Two and a half kilograms of ice [c=2.00 x 10^3J/(kgxC0] are added to the punch. The ice has an initial temperature of -20.0 C, having been kept in a very cold freezer. The punch may be treated as if it were water [c = 4186J/(kgxC)], and it may be assumed that there is no heat flow between the punch bowl and the external environment. The latent heat of fusion for water is 3.35 x 10^5 J/kg. When thermal equilibrium is reached, all the ice has melted, and the final temperature of the mixture is above 0 C. Determine this temperature.

18. Practice Problem 52. To help prevent frost damage, fruit growers sometimes protect their crop by spraying it with water when overnight temperatures are expected to go below the freezing mark. When the water turns to ice during the night, that is released into the plants, thereby giving them a measure of protection against the falling temperature. Suppose a grower sprays 7.2 kg of water at 0 C onto a fruit tree. (a) How much heat is released by the water when it freezes? (b) How much would the temperature of a 180 kg tree rise if it absorbed the heat released in part (a)? Assume that the specific heat capacity of the tree is 2.5 x 10^3 J/kgC and that no phase change occurs within the tree itself.

20. Homework pg. 391 ch. 12 54 56 57 58

21. 12.9 Equilibrium Between Phases of Matter • Under specific conditions of temperature and pressure, a substance can exist at equilibrium in more than one phase at the same time. • Ex. Container kept at a constant temp. by a large reservoir of heated sand. Partially filled with a liquid and a few fast-moving molecules escape the liquid and form a vapor phase. • Molecules pick up the required energy (the latent heat of vaporization) during collisions with neighboring molecules in the liquid.

22. The reservoir of heated sand replenishes the energy carried away, thus maintaining the constant temperature. • At first, the movement of molecules is predominantly from liquid to vapor, although some molecules in the vapor phase do reenter the liquid. • As the molecules accumulate in the vapor, the number reentering the liquid eventually equals the number entering the vapor, at which point equilibrium is established, as in part b. • The concentration of molecules in the vapor phase does not change, and the vapor pressure remains constant. • The pressure of the vapor that coexists in equilibrium with the liquid is called the equilibriumvaporpressure of the liquid.

23. Equilibrium vapor pressure does not depend on the volume of space above the liquid. • If more space were provided, more liquid would vaporize, until equilibrium was reestablished at the same vapor pressure, assuming the same temperature is maintained. • Equilibrium vapor pressure depends only on the temperature of the liquid; a higher temp. causes a higher pressure.

24. Only when the temperature and vapor pressure correspond to a point on the curved line, which is called the vaporpressurecurve or the vaporization curve, do liquid and vapor phases coexist at equilibrium.

25. Boiling to occur, the pressure of the vapor inside them must at least equal the air pressure acting on the surface of the water. • Atmosphere 1.01 x 10^5 Pa • 1.01 x 10^5 Pa corresponds to a temperature of 100 C. • Water boils at 100 C at one atmosphere of pressure. • Liquid boils at the temperature for which its vapor pressure equals the external pressure. • So if the atmospheric pressure goes down the boiling point goes down.

26. Water does boil at 83 C on a mountain at an altitude of just under five kilometers, because atmospheric pressure there is 0.53 x 10^5 Pa.

27. Spray cans lowers the pressure inside the can so that the liquid comes out like a vapor. • For each temperature, there is a single pressure at which the two phases can coexist in equilibrium. • Fusioncurve: a plot of the equilibrium pressure versus equilibrium temperature.

28. 12.10 Humidity • Air is a mixture of gases, including nitrogen, oxygen, and water vapor. • Total pressure of the mixture is the sum of the partial pressures of the component gases. • The partialpressure of a gas is the pressure it would exert if it alone occupied the entire volume at the same temperature as the mixture.

29. The partial pressure of water vapor in air depends on weather conditions. • Relativehumidity: amt. of water vapor is in the air. Ratio of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature. Percent partial pressure of water vapor Relative = equilibrium vapor pressure of x100 Humidity water at the existing temperature

30. Vaporization curve of water gives the equilibrium vapor pressure of water at the existing temperature. • When the partial pressure of the water vapor equals the equilibrium vapor pressure of water at a given temperature, the relative humidity is 100%. • Vapor is said to be saturated because it is present in the maximum amount, as it would be above a pool of liquid at equilibrium in a closed container.

31. If the relative humidity is less than 100%, the water vapor is said to be unsaturated.

32. Example 17: Relative Humidities One day, the partial pressure of water vapor in the air is 2.0 x 10^3 Pa. Using the vaporization curve for water in Figure 12.37, determine the relative humidity if the temperature is (a) 32 C and (b) 21 C.

33. Practice Problem 85. Suppose that air in the human lungs as a temperature of 37 C, and the partial pressure of water vapor has a value of 5.5 x 10^3 Pa. What is the relative humidity in the lungs? Consult the vapor pressure curve for water that accompanies problem 68.

34. 85.

35. 54.