LECTURE 8 PHASES, EVAPORATION & LATENT HEAT Lecture Instructor: Kazumi Tolich Lecture 8 2 ¨ Reading chapter 17.4 to 17.5 ¤ Phase equilibrium ¤ Evaporation ¤ Latent heats n Latent heat of fusion n Latent heat of vaporization n Latent heat of sublimation Phase equilibrium & vapor-pressure curve 3 ¨ If a substance has two or more phases that coexist in a steady and stable fashion, the substance is in phase equilibrium. ¨ The pressure of the gas when equilibrium is reached is called equilibrium vapor pressure. ¨ A plot of the equilibrium vapor pressure versus temperature is called vapor-pressure curve. ¨ A liquid boils at the temperature at which its vapor pressure equals the external pressure. Phase diagram 4 ¨ A fusion curve indicates where the solid and liquid phases are in equilibrium. ¨ A sublimation curve indicates where the solid and gas phases are in equilibrium. ¨ A plot showing a vapor-pressure curve, a fusion curve, and a sublimation curve is called a phase diagram. ¨ The vapor-pressure curve comes to an end at the critical point. Beyond the critical point, there is no distinction between liquid and gas. ¨ At triple point, all three phases, solid, liquid, and gas, are in equilibrium. ¤ In water, the triple point occur at T = 273.16 K and P = 611.2 Pa. Quiz: 1 5 ¨ In most substance, as the pressure increases, the melting temperature of the substance also increases because a solid is denser than the corresponding liquid. But in water, ice is less dense than liquid water. Does the fusion curve of water have a positive or negative slope? A. Positive B. Negative Quiz: 8-1 answer 6 ¨ Negative ¨ In most substances, the fusion line has a positive slope. As the pressure increases, the melting temperature of the substance also increases because a solid is denser than the corresponding liquid. ¨ In water, the slope is negative because ice is less dense. Typical substance Water Example: 1 7 ¨ The phase diagram for water is shown. a) What is the temperature T1? b) What is the temperature T2? c) What happens to the melting/freezing temperature if atmospheric pressure is decreased? d) What happens to the boiling/condensation temperature if atmospheric pressure is increased? Evaporation/ Demo: 1 8 ¨ Evaporation is a cooling process. ¨ Freezing water by evaporation ¤ When the pressure is lowered, water boils at a lower temperature. ¤ Evaporation of water lowers the temperature of water itself. Demo: 2 9 ¨ CO2 sublimation ¤ Demonstration of sublimation of CO2 Latent heats 10 ¨ The energy required to convert a substance of mass � from one phase to another is given by � = �� where � is the coefficient of latent heat. ¤ latent heat of fusion, �%, solid to liquid ¤ latent heat of vaporization, �&, liquid to gas ¤ latent heat of sublimation, �', solid to gas Example: 2 11 ¨ A heat transfer of Q = 9.5 × 105 J is required to convert a block of ice at Ti = -12 °C to Tf = 12 °C. What was the mass of the block of ice? Quiz: 2 12 ¨ Which will cause more severe burns to your skin: 100°C water or 100°C steam of a same mass? A. Water B. Steam C. Both the same Quiz: 8-2 answer 13 ¨ Steam ¨ The hot steam first has to undergo a phase change into water at 100 °C before cooling down. This releases additional energy causing more severe burns. Example: 3 14 ¨ Flesh becomes badly damaged when its temperature reaches 50.0 °C. a) Calculate the heat released as m = 12.5 g of liquid water at Ti = 100 °C is cooled to Tf = 50.0 °C. b) Calculate the heat released as m = 12.5 g of steam at Ti = 100 °C is condensed and cooled to Tf = 50.0 °C. c) Calculate the mass of flesh that can be heated from T’i = 37.0 °C (normal body temperature) to T’f = 50.0 °C. The average specific heat of flesh is cflesh = 3500 J/kg·K. Quiz: 3 15 ¨ You step out of a swimming pool on a hot day, where the air temperature is 90°F. Where will you feel cooler, in Phoenix (dry air) or in Philadelphia (humid air)? A. equally cool in both places B. Philadelphia C. Phoenix Quiz: 8-3 answer 16 ¨ Phoenix ¨ In Phoenix, where the air is dry, more of the water will evaporate from your skin because there is not much water vapor in the air. ¨ Evaporation is a phase change, where the water must absorb the heat of vaporization from your skin. ¨ That is why you feel cool as the water evaporates. ¨ You may also feel colder when you are taking a shower with a bathroom door open compared to when the door is closed. Quiz: 4 17 ¨ The graph shows the temperature of a 1.0-g sample of material as heat is added to it. The material is initially a solid at 10ºC. The pressure remains constant, and there is no chemical change. What is the coefficient of latent heat of fusion for the material in cal/g? Quiz: 8-4 answer 18 ¨ 50 cal/g ¨ The coefficient of latent heat of fusion is the energy required to convert a substance of unit mass from one phase to another. Q Q 50 cal L = = m 1.0 g Quiz: 5 19 ¨ The graph shows the temperature of a 1.0-g sample of material as heat is added to it. The material is initially a solid at 10ºC. The pressure remains constant, and there is no chemical change. What is the specific heat of the solid ()* phase in ? +,-° Quiz: 8-5 answer 20 ()* ¨ 0.25 +,-° ¨ The specific heat is the energy required to raise the temperature of a substance of unit mass by 1C°. Q 0 45 ()* ()* ¨ � = = = 0.25 1,23 4.5 + 85 °- +,-° ΔT Water protects buds from cold weather 21 ¨ When temperature falls a few degrees below 0 °C, fruit crop is in danger of being ruined. ¨ To protect the buds, farmers spray the trees with water. ¨ Water has large latent heat of fusion. ¨ Before the buds can freeze, the water must be cooled to 0 °C and then freeze. ¨ In this process, the water gives up heat and keeps the temperature of the buds from going below 0 °C. ¨ The layer of ice over the buds acts like insulation because ice is not a good conductor of heat..