Lecture 23 Specific Heat and Phase Changes
Today s Topics: Heat and Temperature Change Specific heat Heat and Phase Change Latent heat
Heat and Temperature Change Heat is energy that flows from a higher-temperature object to a lowertemperature object because of a difference in temperatures. SI Unit of Heat: joule (J) The heat that must be supplied or removed to change the temperature of a substance is Q = mcdt specific heat capacity SI Unit for Specific Heat Capacity: J/(kg K)
OTHER ENERGY UNITS 1 kcal = 4186 joules 1 cal = 4.186 joules
Two objects are made of the same material, but have different masses and temperatures. If the objects are brought into thermal contact, which one will have the greater temperature change? ACT: Thermal Contact a) the one with the higher initial temperature b) the one with the lower initial temperature c) the one with the greater mass d) the one with the smaller mass e) the one with the higher specific heat Because the objects are made of the same material, the only difference between them is their mass. The object with less mass will change temperature more easily because not much material is there (compared to the more massive object).
ACT: Two Liquids The same amount of heat is added to two equal-mass liquids, that are initially at the same temperature. You measure the temperatures and find that one liquid has a higher temperature than the other. Which liquid has a higher specific heat? a) the cooler one b) the hotter one c) both the same Both liquids had the same increase in internal energy, because the same heat was added. But the cooler liquid had a smaller temperature change. Because Q = mc T, if Q and m are both the same and T is smaller, then c (specific heat) must be bigger.
ACT: Night on the Field The specific heat of concrete is greater than that of soil. A baseball field (with real soil) and the surrounding parking lot are warmed up during a sunny day. Which would you expect to cool off faster in the evening when the sun goes down? a) the concrete parking lot b) the baseball field c) both cool off equally fast The baseball field, with the lower specific heat, will change temperature more readily, so it will cool off faster. The high specific heat of concrete allows it to retain heat better and so it will not cool off so quickly it has a higher thermal inertia.
Calorimetry If there is no heat loss to the surroundings, the heat lost by the hotter object equals the heat gained by the cooler ones.
Calorimetry 1 kg of water at 100 C is poured into a bucket that contains 4 kg of water at 0 C. Find the equilibrium temperature (neglect the influence of the bucket). a) 0 C b) 20 C c) 50 C d) 80 C e) 100 C Because the cold water mass is greater, it will have a smaller temperature change! The masses of cold/hot have a ratio of 4:1, so the temperature change must have a ratio of 1:4 (cold/hot). Q 1 = -Q 2 m 1 cδt 1 = -m 2 cδt 2 ΔT 1 / ΔT 2 = m 2 / m 1
Example: Heat and Temperature Two spheres, labeled A and B, have identical masses, but are made of different substances. The specific heat capacity of sphere A is c A = 440 J/(kg o C) and that of sphere B is c B = 160 J/(kg o C). The spheres are initially at 21 o C; and the same quantity of heat is added to each sphere. If the final temperature of sphere A is 72 o C, what is the final temperature of sphere B?
Example A 0.20-kg lead ball is heated to 90.0 o C and dropped into an ideal calorimeter containing 0.50 kg of water initially at 20.0 o C. What is the final equilibrium temperature of the lead ball? The specific heat capacity of lead is 128 J/(kg o C); and the specific heat of water is 4186 J/(kg o C).
The calorimeter is made of 0.15 kg of aluminum and contains 0.20 kg of water. Initially, the water and cup have the same temperature of 18.0 o C. A 0.040 kg mass of unknown material is heated to a temperature of 97.0 o C and then added to the water. After thermal equilibrium is reached, the temperature of the water, the cup, and the material is 22.0 o C. Ignoring the small amount of heat gained by the thermometer, find the specific heat capacity of the unknown material. c unknown = ( mcdt ) Al + ( mcdt ) ( mdt ) unknown water c unknown = 2!!!! [ 9.00 10 J ( kg C )]( 0.15 kg)( 4.0 C ) + [ 4186 J ( kg C )]( 0.20 kg)( 4.0 C )! ( 0.040 kg)( 75.0 C ) c unknown = 1300 J! ( kg C )
Heat and Phase Changes THE PHASES OF MATTER During a phase change, the temperature of the mixture does not change (provided the system is in thermal equilibrium).
Latent Heat The heat that must be supplied or removed to change the phase of a mass m of a substance is SI Units of Latent Heat: J/kg latent heat
Solving problems involving phase changes is similar to solving problems involving heat transfer, except that the latent heat must be included as well.
Example A thermos bottle contains 3.0 kg of water and 2.0 kg of ice in thermal equilibrium at 0 o C. How much heat is required to bring the system to thermal equilibrium at 50 o C?
ACT: Adding Heat If you add some heat to a substance, is it possible for the temperature of the substance to remain unchanged? a) yes b) no Yes, it is indeed possible for the temperature to stay the same. This is precisely what occurs during a phase change the added heat goes into changing the state of the substance (from solid to liquid or from liquid to gas) and does not go into changing the temperature! Once the phase change has been accomplished, then the temperature of the substance will rise with more added heat.
ACT: Hot Potato Will potatoes cook faster if the water is boiling faster? a) yes b) no The water boils at 100 C and remains at that temperature until all of the water has been changed into steam. Only then will the steam increase in temperature. Because the water stays at the same temperature, regardless of how fast it is boiling, the potatoes will not cook any faster.
ACT: Spring Break 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) or in Philadelphia (humid)? a) equally cool in both places b) Philadelphia c) Phoenix In Phoenix, where the air is dry, more of the water will evaporate from your skin. This is a phase change, where the water must absorb the heat of vaporization, which it takes from your skin. That is why you feel cool as the water evaporates.
You re in Hot Water! Which will cause more severe burns to your skin: 100 o C water or 100 o C steam? a) water b) steam c) both the same d) it depends... Although the water is indeed hot, it releases only 1 cal/(g o C) of heat as it cools. The steam, however, first has to undergo a phase change into water and that process releases 540 cal/g, which is a very large amount of heat. That immense release of heat is what makes steam burns so dangerous.