1. Heat Today’s Big Three: 1.Heat transfer 2.Specific heat 3.Latent heat of fusion

2. Heat Definition: Flow of energy between two objects due to difference in temperature – Note: similar to WORK – Object does not “have” heat (it has energy: temp) Energy is exchanged (heat is transferred) through various mechanism: – Radiation – collisions – convection. Units: Joule – 4186 Joules = 1 Calorie = 1000 calories = – calorie: Amount of heat needed to raise 1g of water 1ºC 10

3. Example: Sears Tower You decide to take the stairs to the top of the Sears tower (442m). If you have a weight of 670N and your body was 100% efficient in converting food into mechanical energy. How many Calories would you need to eat to replenish your body Whopper with Cheese: 696 Cal Big Mac with Cheese: 560 Cal

4. Temperature Temperature: measure of average translational Kinetic Energy of molecules Two bodies at different temperature in contact: Both bodies will equilibrate to one common temperature.

5. Temperature Why do substances at different temperatures equilibrate? Elastic collision between fast (high kinetic energy) and slow (low kinetic energy) atoms, result in energy transfer to slow atoms.

6. Temperature What happens to the transferred energy? Depending on the possible energetic states of the body, it is transformed into translational, rotational, vibration energy of its atoms and molecules: The amount of heat required to increase a body’s temperature (translational energy of its molecules) depends on how this heat is used: All heat transferred to translational energy or heat transferred to several modes of energy.

7. Question: Compare two gases: One is a mono-atomic gas, the other is a diatomic gas which in addition to its translational energy has energetic states as shown below. Which gas requires more energy per number of particles to raise the temperature by the same amount? A) mono-atomic gas B) diatomic gas C)Both the same

8. Specific Heat Heat adds energy to object/system IF system does NO work then: – Heat increases internal energy. Q =  U – Heat increases temperature! Q = c m  T – Heat required to increase Temp depends on amount of material (m) and type of material (c) Q = cm  T : “Cause” = “inertia” x “effect” (just like F=ma) – cause = Q – effect =  T – inertia = cm (mass x specific heat capacity)  T = Q/cm (just like a = F/m) 15

9. Act After a grueling work out, you drink a liter of cold water (0 C). How many Calories does it take for your body to raise the water up to body temperature of 36 C? (calorie: Amount of heat needed to raise 1g of water 1ºC) 1) 36 2) 360 3) 3,600 4) 36,000 1 liter = 1,000 grams of H 2 0 1000 g x 1 calorie/(gram degree) x (36 degree) = 36,000 calories 36,000 calories = 36 Calories! 18

10. Heat transfer Objects with different temperatures are brought into contact. There final temperatures will be the same. Energy conservation applies: Q 1 +Q 2 +Q 3 +…=0 ΔT 1 c 1 m 1 + ΔT 2 c 2 m 2 + ΔT 3 c 3 m 3 +…=0 (T f -T 1 ) c 1 m 1 + (T f -T 2 ) c 2 m 2 + (T f -T 3 ) c 3 m 3 +…=0

11. Specific Heat ACT Suppose you have equal masses of aluminum and copper at the same initial temperature. You add 1000 J of heat to each of them. Which one ends up at the higher final temperature A) aluminum B) copper C) the same  T = Q/cm 23 Substance c in J/(kg-C) aluminum900 copper387 iron452 lead128 human body 3500 water 4186 ice 2000

12. Question 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 20 Substance c in J/(kg-C) aluminum900 copper387

13. Ponderable: Heat capacity An aluminum cup has mass 300g and contains 200ml of water. Both are at room temperature (20 0 C )and the cup is insulated from the environment with a styrophor sleeve. Then you drop a 100 0 C hot piece of copper which has 200g mass in your cup. Now you put a styrophor lid on the cup and wait a couple of minutes What is the approximate final temperature of your cup, water and piece of copper?

14. In this experiment we will measure the specific heat of some metal specimens. The basic procedure is as follows: Heat the specimen to a high temperature by suspending it in boiling water. Place the specimen in water at low temperature in the calorimeter. Measure the equilibrium temperature in the calorimeter. From the initial and final temperatures, and from the masses of the metal, the water, and the calorimeter cup, we can calculate the metal’s specific heat.. Some sources of error in this experiment, which you should take steps to minimize, are as follows: First, our calorimeters are not perfect, and heat flow into or out of the calorimeter will occur. Experience shows that the final temperature in this experiment will be about 4-6  C above room temperature. We will “split the difference” of the unwanted heat flow by starting with water about 5  C below room temperature. Then heat that flows out of the calorimeter when the water is hotter than room temperature will be approximately offset by heat that flows into the calorimeter when the water is cooler than room temperature. Secondly, temperature gradients in the calorimeter and even in the boiling water are inevitable, so that a quick measurement of temperature (either with a thermometer or a temperature sensor) may not reflect the average temperature in the water. You should gently stir the water with your temperature probe before taking the measurement – gently, so that the stirring itself does not raise the temperature of the water. Experiment 1

15. Equipment Calorimeter Steam generator Metal specimens Digital thermometer, or temperature sensor Glass beaker Table stand Support rod String Ice Paper towels or cloths

16. 1.Heat the metal. Fill the steam generator about ¾ full with water. Turn on the power and turn the knob to full. (Be careful of the steam and the hot water when the water boils. Arrange things so that the generator will be out of your way when you transfer the cube into the calorimeter.) Weigh the specimen to be measured and record the mass in the data table. Also record the metal and/or a description of the metal for identification purposes. Attach a support rod to a table stand. Get a piece of string about 30 cm long. Tie the metal specimen to one end, then run the other end through the hole in the calorimeter lid. Finally, wrap the free end of the string around the support rod. Perch the calorimeter lid on the end of the support rod to keep it out of the way temporarily. (The purpose here is to have the lid ready to be placed on the calorimeter, with the string already running through it.) Suspend the metal in the water in the generator so that the top of the specimen is slightly above the surface of the water. Try to keep the top dry so that you do not pull out hot water when you transfer the specimen to the calorimeter. The specimen should be fully submerged and should not touch the sides or bottom of the generator. Let the water come to a boil. Meanwhile, perform steps 2, 3 and 4.

17. 2.Weigh the calorimeter cup. Take the small cup out of the calorimeter and weight it. Record its mass. 3.Mix up some cool water. Using a beaker, get a supply of cold water from the ice water supply provided. Make sure there is no ice in your cold water. Fill the calorimeter cup about ½ full with tap water. Then add cold water (with no ice) and stir, until the calorimeter water is about 5 degrees below room temperature. (Use the digital thermometer to measure room temperature. Note: don’t assume room temperature will remain the same throughout the lab session. It won’t.) 4.Weigh the calorimeter cup with the water in it. Weigh the cup with the cool water in it. The difference between this mass and the mass of the cup alone is the mass of the water, which you will use in the calculation. Record the mass of the water in the data table. Place the calorimeter cup in the calorimeter. Use a cloth or paper towel as a temporary lid for the calorimeter to keep the water cool. (You can always readjust the temperature of the water by adding more cold water. But then you must weigh the water again.)

18. 5.Take the initial temperature readings After the water in the steam generator boils, but before transferring the metal, measure the temperature of the cool water in the calorimeter. Gently stir the water with the probe of the digital thermometer, then take the reading to the nearest 1/10 degree C. Record this as the initial temperature of the water, T 1. Measure the temperature of the boiling water. Stir the water with the thermometer’s probe first, then read the temperature to the nearest 1/10 degree C. Record this as the initial temperature of the metal, T 2. (Since the metal is in thermal equilibrium with the boiling water, it should have the same temperature.) 6.Transfer the metal to the calorimeter. The best way to do this is to lift the metal out of the generator by the string, swivel the support rod or move the table stand, then lower the cube into the calorimeter. Then put the calorimeter lid in place. Note: While transferring, shake or brush off any hot water droplets that adhere to the specimen. You do not want to transfer any hot water. Make sure the metal is fully submerged and is not touching the sides or bottom of the calorimeter. 7.Measure the final (equilibrium) temperature After the temperature in the calorimeter stops changing, gently stir the water with the thermometer probe. Measure the temperature to the nearest 1/10 degree C and record this as the final temperature of the system, T f.

19. Latent Heat L As you add heat to water, the temperature increases for a while, then it remains constant, despite the additional heat! Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid- gas). 28 T Q added to water water temp rises water changes to steam (boils) steam temp rises 100 o C Latent Heat Substance L f (J/kg) L v (J/kg) water33.5 x 10 4 22.6 x 10 5

20. Ice Act Which will do a better job cooling your soda, a “cooler” filled with water at 0C, or a cooler filled with ice at 0 C. A) WaterB) About SameC) Ice T Q added to water ice temp rises ice changes to water (melts) water temp rises 0 o C Latent Heat Substance L f (J/kg) L v (J/kg) water33.5 x 10 4 22.6 x 10 5 Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid-gas). 30

21. Ponderable: sweat During a tough work out, your body sweats (and evaporates) 1 liter of water to keep cool (37 C). How much water would you need to drink (at 2C) to achieve the same thermal cooling? (recall C V = 4.2 J/g-C for water, L v =2.2x10 3 J/g) 33

22. Question 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? 35

23. Ponderable: ice and water How much ice (at 0 C) do you need to add to 0.5 liters of a water at 25 C, to cool it down to 10 C? (L = 80 cal/g, c = 1 cal/g C, c ice = 0.5 cal/g C)

24. Ponderable: ice and water 2 0.8kg of ice (at -10 o C) is added to 1.4kg of water at 20 o C. How much of the ice will melt? (L f = 33.5x10 4 J/kg, c water = 4186 J/kg C, c ice = 2000 J/kg C)

25. Ponderable: Latent heat An aluminium cup has mass 300g and contains 200ml of water. Both are at room temperature (20 0 C )and the cup is insulated from the environment with a styrophor sleeve. Then you drop 20g of ice in your cup. Now you put a styrophor lid on the cup and wait a couple of minutes What is the approximate final temperature of your cup and water?

26. In this experiment we will measure the Latent Heat of Fusion of water. We will put some ice in a calorimeter along with some warm water. From the initial and final temperatures, and from the masses of the ice, water and calorimeter cup, the latent heat can be calculated. As in the specific heat experiment, we will “split the difference” by starting with water about 10  C above room temperature. We will put enough ice in the calorimeter to reduce the temperature to 10  C below room temperature. We will assume the temperature of the ice is 0  C. Experiment 2

27. Equipment Calorimeter Steam generator Digital thermometer, or temperature sensor Glass beaker Ice Paper towels or cloths Procedures 1. Weigh the empty calorimeter cup and record its mass. 2..Mix warm water in the beaker. Siphon off some hot water from the steam generator’s reservoir and mix this with tap water until the mixture is about 10  C above room temperature. 3.Pour about 100 grams of warm water into the calorimeter cup. Weigh the water and cup and record the total mass. Put the calorimeter cup into the calorimeter. 4.Put about 25 grams of ice on a towel or cloth. Just before putting the ice into the calorimeter, dry the ice as much as possible. 5.Measure the initial temperature of the water in the calorimeter and record it. 6.Pour the ice into the calorimeter. The temperature of the mixture should go about 10  C below room temperature. 7.Weigh the calorimeter with the ice and water. 8.Record the equilibrium temperature after the ice is completely melted. Stir the water to ensure it is uniform.