1. Heat and Energy Lecturer: Professor Stephen T. Thornton

2. Reading Quiz A 5-kg cube of hot steel is put in thermal contact with a 10-kg cube of cold steel. Which of the following statements is most valid: A) Heat flows from the larger cube to the smaller one, because the larger cube has the most internal energy. B) Heat flows from the warmer cube to the colder one until they have the same heat content. C) Heat flows from the warmer cube to the colder one until they have the same temperature. D) Heat transfers until both cubes have the same heat.

3. Reading Quiz Answer: C Heat content is a misnomer. Heat does not flow to make the internal energy the same, but rather to make the temperature the same.

4. Last Time Kinetic energy of molecules Maxwell distribution Phase changes Vapor pressure and humidity Van de Waals Equation Mean free path Diffusion

5. Today Heat Internal energy Specific heat Latent heat First Law of Thermodynamics

6. Heat and mechanical work At one time it was thought that all substances contained a heat fluid or “caloric” that could flow from one substance to another. The American royalist Benjamin Thompson (Count Rumford) finally figured out while boring cannons that friction caused heat flow, which is a form of energy. Doing work causes heat flow, so they should be related.

7. Copyright © 2009 Pearson Education, Inc. We often speak of heat as though it were a material that flows from one object to another; it is not. Rather, it is a form of energy flow. Unit of heat: calorie (cal) 1 cal is the amount of heat necessary to raise the temperature of 1 g of water by 1 Celsius degree. Don’t be fooled—the calories on our food labels are really kilocalories (kcal or Calories), the heat necessary to raise 1 kg of water by 1 Celsius degree. Heat as Energy Transfer

8. Copyright © 2009 Pearson Education, Inc. Definition of heat: Heat is energy transferred from one object to another because of a difference in temperature. Remember that the temperature of a gas is a measure of the kinetic energy of its molecules. Heat as Energy Transfer

9. Mechanical equivalent of heat British physicist James Joule did experiment in mid-1800s to determine how heat is related to work and energy. Now we know Q = heat flow = energy transferred due to temperature differences.

10. The Mechanical Equivalent of Heat

11. Copyright © 2009 Pearson Education, Inc. The sum total of all the energy of all the molecules in a substance is its internal (or thermal) energy. Temperature: measures molecules’ average kinetic energy Internal energy: total energy of all molecules Heat: transfer of energy due to difference in temperature Internal Energy

12. Copyright © 2009 Pearson Education, Inc. Internal energy of an ideal (monoatomic) gas (that is, its translational KE): But since we know the average kinetic energy in terms of the temperature, we can write: We often denote internal energy by U.

13. Copyright © 2009 Pearson Education, Inc. If the gas is molecular rather than atomic, rotational and vibrational kinetic energy need to be taken into account as well. Internal Energy

14. What happens if we add pieces (same volume) of hot metal to Styrofoam cups with equal amounts of water at the same temperature? Aluminum and copper Do experiment. Use thermometers and TV. Drop two pieces of metal at 100 0 C into two cups containing room temperature water.

15. We find that the result depends on the metal (note final temperatures). Aluminum and copper are different. Why? We know that it takes 1 cal of heat energy to raise the temperature of water by 1 0 C.

16. Heat capacity We find that every substance has a specific property of heat capacity C: Q is positive or negative depending on whether heat energy is added or removed from the object.

17. Specific heat Heat capacity is not so useful because we must specify type of substance and how much. We define a new quantity, called specific heat, that depends on the particular substance.

18. Copyright © 2009 Pearson Education, Inc. The amount of heat required to change the temperature of a material is proportional to the mass, specific heat, and temperature change: The specific heat, c, is characteristic of the material. Some values are listed at left. Specific Heat

19. 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? 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 Conceptual Quiz

20. 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? 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. Clearly, the object with less mass will change temperature more easily because not much material is there (compared to the more massive object). Conceptual Quiz

21. Two different objects receive the same amount of heat. Which of the following choices is NOT a reason why the objects may have different temperature changes? A) they have different initial temperatures B) they have different masses C) they have different specific heats Conceptual Quiz

22. Two different objects receive the same amount of heat. Which of the following choices is NOT a reason why the objects may have different temperature changes? A) they have different initial temperatures B) they have different masses C) they have different specific heats Q = m c  T Because Q = m c  T and the objects received the same amount of heat, the only other factors are the masses and the specific heats. Although the initial temperature is certainly relevant for finding the final temperature, it does not have any effect on the temperature change  T. Conceptual Quiz

23. Calorimetry We dropped 2 blocks of hot metal into Styrofoam cups of water. Calculate the final temperature. Q metal + Q water = 0 Q m is the heat flow to metal (negative). Q w is the heat flow to water (positive). The metal loses heat energy to the water. There is a flow of heat energy from the metal to the water. The metal cools, and the water is hotter. Sometimes I simply use Q(lost) = Q(gained)

25. Consider previous experiment Q Cu = m Cu c Cu ΔT = (0.0485 kg)(387 J/kg K) ΔT = 18.8 ΔT J Q Al = m Al c Al ΔT = (0.0147 kg)(900 J/kg K) ΔT = 13.2 ΔT J The Q metal will be transferred to raise the water temperature. Which metal raised the temperature the most?

26. Latent heat L is the energy/kg needed to change the phase state of matter. Latent heat of fusion L F is energy/kg needed to melt a substance; solid goes to liquid. Latent heat of vaporization L V is energy/kg needed to go from liquid to gas. Latent heat of sublimation L S is energy/kg required to go from solid directly to gas.

27. Copyright © 2009 Pearson Education, Inc. Energy is required for a material to change phase, even though its temperature is not changing. Latent Heat 1 kg L f = 80 cal/g L v = 539 cal/g = 539 kcal/kg

29. Copyright © 2009 Pearson Education, Inc. The latent heat of vaporization is relevant for evaporation as well as boiling. The heat of vaporization of water rises slightly as the temperature decreases. On a molecular level, the heat added during a change of state does not go to increasing the kinetic energy of individual molecules, but rather to breaking the close bonds between them so the next phase can occur. Latent Heat

30. Will potatoes cook faster if the water is boiling faster? A) yes B) no C) depends on W Conceptual Quiz

31. Will potatoes cook faster if the water is boiling faster? A) yes B) no C) depends on W 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. Since the water stays at the same temperature, regardless of how fast it is boiling, the potatoes will not cook any faster. Conceptual Quiz Follow-up: Follow-up: How can you cook the potatoes faster?

32. Conceptual Quiz You put 1 kg of ice at 0 o C together with 1 kg of water at 50 o C. What is the final temperature? çL F = 80 cal/g çc water = 1 cal/g o C A) 0 o C B) between 0 o C and 50 o C C) 50 o C D) greater than 50 o C

33. How much heat is needed to melt the ice? Q = m L f = (1000g)  (80 cal/g) = 80,000 cal How much heat can the water deliver by cooling from 50 o C to 0 o C? Q = c water m  T = (1 cal/g o C)  (1000g)  (50 o C) = 50,000 cal Thus, there is not enough heat available to melt all the ice!! Conceptual Quiz You put 1 kg of ice at 0 o C together with 1 kg of water at 50 o C. What is the final temperature? çL F = 80 cal/g çc water = 1 cal/g o C A) 0 o C B) between 0 o C and 50 o C C) 50 o C D) greater than 50 o C Follow-up: Follow-up: How much more water at 50 o C would you need?

34. Conceptual Quiz Which will cause more severe burns to your skin: 100 °C water or 100 °C steam? A) water B) steam C) both the same D) it depends...

35. 1 cal/g phase change 540 cal/g While the water is indeed hot, it releases only 1 cal/g 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. Conceptual Quiz Which will cause more severe burns to your skin: 100 °C water or 100 °C steam? A) water B) steam C) both the same D) it depends...

36. Consider a system: Automobile engine Human body Simple piston and cylinder We want to consider what happens if we add heat to our system or take heat away. Also let the system do work or have work done on it. What happens to internal energy? The internal energy is the sum of all the kinetic and potential energies.

37. The Internal Energy of a System If we add heat Q to a system having internal energy E i, the new internal energy of the system is E f = E i + Q.  E = E f – E i = Q EiEi E f = E i + Q

38. Work and Internal Energy If the system does work W on the outside, then the system loses internal energy. E i – E f = W  E = E f – E i = -W Ei Ei E f = E i -W

39. First Law of Thermodynamics (Conservation of Energy) Let’s combine the last two equations:  E = E f – E i = Q  E = E f – E i = -W Because both heat flow and work can occur, the change in internal energy of a system depends on both Q and W. First law of thermodynamics

40. Signs of Q and W *** Q positiveSystem gains heat Q negativeSystem loses heat W positiveWork done by system W negativeWork done on system The convention for W is opposite of that in chemistry.

41. The internal energy E depends on the state of the system (P, V, T, m, n). They are called state functions. Heat flow Q and work W are not state functions. They depend on how the system is changed.