10-3: Changes in Temperature and Phase Objectives: Perform calculations with specific heat capacity. Perform calculations involving latent heat. Interpret the various sections of a heating curve. Specific Heat and Capacity Have you ever noticed on a hot day that you jump in a pool and it is much cooler than the air? Why is that? Partly due to evaporation which allows some energy to be removed from the water. Each substance has a unique value for the energy required to change the temperature of 1 kg of that substance by 1C at constant pressure. This value, known as the specific heat capacity (or more commonly just specific heat) of the substance, relates mass, temperature change, and energy transferred as heat. Specific Heat and Capacity Specific heat= Energy Transferred as Heat Mass x Change in temperature The subscript p indicates that the specific heat capacity is measured at constant pressure. Note that a temperature change of 1C is equal in magnitude to a temperature change of 1 K, so that T gives the temperature change in either scale. Specific Heat When the temperature increases, T and Q are taken to be positive, which corresponds to energy transferred into the substance. Likewise, when the temperature decreases, T and Q are negative and energy is transferred from the substance. Table 10-4 Shows the specific heat of some substances. Determining specific heat capacity To measure the specific heat capacity of a substance, it is necessary to measure mass, temperature change, and energy transferred as heat. It is hard to measure the amount of heat. However, the specific heat capacity of water (4.186 kJ/kgC) is known, so the energy transferred as heat between an object of unknown specific heat capacity and a known quantity of water can be measured. When a warm object is placed in cool water the energy will transfer from the object to the water. Some may be absorbed by the container, but we are not going to take that into account in this class. energy absorbed by water = energy released by the substance Q w = Q x Q=c p mT CP= Specific heat capacity, m=mass, T= Change in temp. c p,w m w T w = c p,x m x T x (always write the change in temp as a positive) Determining specific heat capacity Calorimetry This approach to determining a substances specific heat capacity is called calorimetry, and devices that are used for making this measurement are called calorimeters. P.372 figure 10-12 A kg metal bolt is heated to an unknown initial temperature. It is then dropped into a beaker containing 0.15 kg of water with an initial temperature of 21.0C. The bolt and the water then reach a final temperature of 25.0C. If the metal has a specific heat capacity of 899 J/kgC, find the initial temperature of the metal. Given: m metal = m m = kg m water = m w = 0.15 kg T water = T w = 21.0C c p,m = 899 J/kgC c p,w = 4186 J/kgC T final = T f = 25.0C Unknown: T metal =T m =? c p,w m w T w = c p,x m x T x (4186 J/kg *C)(0.15 kg)(4.0C)= (899 J/kg*C)(0.050 kg)(T m ) ( J*C 2 ) = (44.95 J*C) (T m ) T m =55.88 C Find T m,i = T m + T m,f T m,i = (55.88 C)+(25.0 C) T m,i = 81 C Assignment Practice 10C page 374 Questions 1-5 Latent Heat Look at the graph (10-13) on page 376. Notice as energy is added the temperature goes up until it hits 0C (segment A). Notice at 0C the amount of energy goes up but the temperature does not. Instead, the nature of the ice changes. The ice begins to melt and change into water at 0C (segment B). The ice-and-water mixture remains at this temperature until all of the ice melts. From 0C to 100C, the waters temperature steadily increases (segment C). At 100C, however, the temperature stops rising and the water turns into steam (segment D). Once the water has completely vaporized, the temperature of the steam increases (segment E). Steam whose temperature is greater than the boiling point of water is referred to as superheated. Latent Heat Phase Change When substances melt, freeze, boil, condense, or sublime (change from a solid to vapor or from vapor to a solid), the energy added or removed changes the internal energy of the substance without changing its temperature. These changes in matter are called phase changes. The existence of phase changes requires that the definition of heat be expanded. Heat is the energy that is exchanged between two objects at different temperatures or between two objects at the same temperature when one of them is undergoing a phase change. Phase changes involve potential energy between particles Particles have a certain amount of potential energy when spaced apart. As they become spaced farther apart that amount increases, until the bond between them breaks. Think of a rubber band being stretched. Energy required to melt a substance goes into rearranging the molecules Phase changes result from a change in the potential energy between particles of a substance. When energy is added to or removed from a substance undergoing a phase change, the particles of the substance rearrange themselves to make up for their change of energy. If ice is melting, the absorbed energy is sufficient to break the weak bonds that hold the water molecules together as a well- ordered crystal. New but different bonds form between the liquid water molecules that have separated from the crystal, so some of the absorbed energy is released again. The difference between the potential energies of the broken bonds and the newly formed bonds is equal to the net energy added to the ice. Heat of fusion the energy per unit mass transferred in order to change a substance from solid to liquid or from liquid to solid at constant temperature and pressure Units are j/kg Section B on figure 10-13 Heat of vaporization The energy per unit mass transferred in order to change a substance from liquid to vapor or from vapor to liquid at constant temperature and pressure Units are J/kg Section D on Figure 10-13 Latent heat The energy per unit mass that is transferred during a phase change of a substance Energy transferred as heat during a phase change = mass latent heat Q = mL For calculations involving melting or freezing, the latent heat of fusion is noted by the symbol L f. Similarly, for calculations involving vaporizing or condensing, the symbol L v is used for latent heat of vaporization. Table 10-6 lists latent heats for a few substances. How much energy is removed when 10.0 g of water is cooled from steam at 133.0C to liquid at 53.0C? There are three times that there is energy transferred in this problem. Look at the diagram on page 380. Steam cools from 133.0C to 100.0C Q S = mc p,s T Steam condenses to form liquid water at 100.0C (Phase change) Q P =mL v Liquid water cools from 100.0C to 53.0C Q L = mc p,w T Q total = Q S + Q P + Q L Given: T steam = T s = C T water = T w = 53.0C c p,steam = c p,s = 2.01 10 3 J/kg C c p,water = c p,w = 10 3 J/kg C L v = 2.26 10 6 J/kg m = 10.0g = 10.0 10 3 kg Unknown: Q total = ? Assignment Page 382 Questions 1-4 Question 1: c p,w m w T w = c p,g m g T g On question 4. When the graph plateaus the first time is at 80.0C. Then at 300.0C, and at the end is at 400.0C. L f = Q/m, and L v =Q/m, and 80.0C 300C 400C