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Chapter 14 Heat

Chapter 14 Heat. Chapter 14: Heat 14.1 Internal energy 14.2 Heat 14.3 Heat capacity and specific heat 14.4 Specific heat of ideal gases 14.5 Phase transitions 14.6 Conduction 14.7 Convection 14.8 Radiation. Internal Energy.

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Chapter 14 Heat

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  1. Chapter 14 Heat

  2. Chapter 14: Heat 14.1 Internal energy 14.2 Heat 14.3 Heat capacity and specific heat 14.4 Specific heat of ideal gases 14.5 Phase transitions 14.6 Conduction 14.7 Convection 14.8 Radiation Ch14c-Heat-Revised-4/25/10

  3. Ch14c-Heat-Revised-4/25/10

  4. Internal Energy The internal energy of a system is the sum total of all the energy of all the molecules in the system. It does not include macroscopic kinetic energy nor energy due to external interactions (potential energy). Ch14c-Heat-Revised-4/25/10

  5. Internal energy includes: • Translational and rotational kinetic energy of the particles due to their individual motions. • Vibrational kinetic and potential energy • Potential energy due to interactions between particles in the system. • Chemical and nuclear energy (binding energies) Ch14c-Heat-Revised-4/25/10

  6. Internal Degrees of Freedom Ch14c-Heat-Revised-4/25/10

  7. Internal energy does not include: • The kinetic energy of the molecules due to translations, rotations, and vibrations of the whole or large fraction of the system. • Potential energy due to the interactions of the molecules of the system with bodies outside of the system (external interactions). Ch14c-Heat-Revised-4/25/10

  8. U = mgh KE = 0 1.7 m U = 0 KE = 0 Example (text problem 14.5): A child of mass 15 kg climbs to the top of a slide that is 1.7 m above a horizontal run that extends for 0.5 m at the base of the slide. After sliding down, the child comes to rest just before reaching the very end of the horizontal portion of the slide. How much mechanical energy was transfered to internal energy during this process? Ch14c-Heat-Revised-4/25/10

  9. Example continued: The change in mechanical energy of the child is E = Ef  Ei = mgh = 250 J. This is the increase in internal energy and is distributed between the child, the slide, and the air. Ch14c-Heat-Revised-4/25/10

  10. Heat Energy Heat is energy in transit between two systems at different temperatures. Heat spontaneously flows from the system at the higher temperature to the system at the lower temperature. Ch14c-Heat-Revised-4/25/10

  11. Heat Energy Experiments by Joule showed the equivalence of Work and Energy A quantity of work done on a system causes the same increase in that system’s internal energy as an identical quantity of heat flowing into the system. Heat is measured in joules or calories. 1 cal = 4.186 J (the mechanical equivalent of heat); 1 Calorie (used on food packaging) = 1 kcal. Ch14c-Heat-Revised-4/25/10

  12. Heat Capacity and Specific Heat For many substances, under normal circumstances TQ. Or Q = CT where C is the heat capacity. The specific heat capacity, or just specific heat, of a substanceis the heat capacity per unit mass. or Ch14c-Heat-Revised-4/25/10

  13. Example (text problem 14.12): 125.6 kJ of heat are supplied to 5.00102 g of water at 22 C. What is the final temperature of the water? Ch14c-Heat-Revised-4/25/10

  14. Example (text problem 14.19): A 0.400 kg aluminum tea kettle contains 2.00 kg of water at 15.0 C. How much heat is required to raise the temperature of the water (and kettle) to 100 C? The heat needed to raise the temperature of the water to Tf is The heat needed to raise the temperature of the aluminum to Tf is Then Qtotal = Qw + QAl = 732 kJ. Ch14c-Heat-Revised-4/25/10

  15. Specific Heat of Ideal Gases The average kinetic energy of a molecule in an ideal gas is And the total kinetic energy of the gas is Ch14c-Heat-Revised-4/25/10

  16. The molar specific heat at constant volume is defined below; this is the heat capacity per mole. Heat is allowed to flow into a gas, but the gas is not allowed to expand. If the gas is ideal and monatomic, the heat goes into increasing the average kinetic energy of the particles. Ideal gas conditions will prevail if we keep the gas density low enough. Examples of monatomic gases are the noble gases such as He, Ne, Ar, Xe; they have no internal degrees of freedom with which to share the energy. Therefore, it all goes into the three translational degrees of freedom. Ch14c-Heat-Revised-4/25/10

  17. Specific Heats and Molar Specific Heats Ch14c-Heat-Revised-4/25/10

  18. Molar Heat Capacities Ch14c-Heat-Revised-4/25/10

  19. Internal Degrees of Freedom This shows the effects of internal degrees of freedom on the specific heat at constant volume for a gas of polyatomic atoms. Below T = 75K the behavior would be similar to that of a monatomic atom. Ch14c-Heat-Revised-4/25/10

  20. The amount of added heat is If the gas is diatomic: Ch14c-Heat-Revised-4/25/10

  21. Internal energy will be distributed equally among all possible degrees of freedom (equipartition of energy). Each degree of freedom contributes ½kT of energy per molecule and ½R to the molar specific heat at constant volume. Rotational motions of a 2-atom molecule: Ch14c-Heat-Revised-4/25/10

  22. Example (text problem 14.26): A container of nitrogen gas (N2) at 23 C contains 425 L at a pressure of 3.5 atm. If 26.6 kJ of heat are added to the container, what will be the new temperature of the gas? For a diatomic gas, The number of moles n is given by the ideal gas law Ch14c-Heat-Revised-4/25/10

  23. Example continued: The change in temperature is The final temperature of the gas is Tf = Ti + T = 317 K = 44 C. Ch14c-Heat-Revised-4/25/10

  24. Phase Transitions A phase transition occurs whenever a substance changes from one phase (solid, liquid, or gas) to another. Ch14c-Heat-Revised-4/25/10

  25. Latent heat is the amount of heat per unit mass required to change the phase of a substance. The energy is used to form/break chemical bonds. The latent heat of fusion (Lf) is the heat per unit mass needed to produce the solid-liquid phase transition. The latent heat of vaporization (Lv) is the heat per unit mass needed to produce the liquid-gas phase transition. Ch14c-Heat-Revised-4/25/10

  26. Example (R&S 6): A 75 g cube of ice at 10.0 C is placed in 0.500 kg of water at 50.0 C in an insulating container so that no heat is lost to the environment. Will the ice melt completely? What will be the final temperature of this system? The heat required to completely melt the ice is The heat required to cool the water to the freezing point is Ch14c-Heat-Revised-4/25/10

  27. Example continued: Since Qice < Qwater the ice will completely melt. To find the final temperature of the system, note that no heat is lost to the environment; the heat lost by the water is gained by the ice. This is the tricky term All ΔT factors are Tf -Ti Ch14c-Heat-Revised-4/25/10

  28. Energy Gained = Energy Lost This term is now positive Advantage - all terms start out as positive amount of energy Ch14c-Heat-Revised-4/25/10

  29. Example (text problem 14.45): The specific heat of the solid is 0.129 kJ/kg K. Assume 31.15 kJ will change 0.500 kg of the solid at 21 C to liquid at 327 C, the melting point. Compute the heat of fusion of a substance from these data. Ch14c-Heat-Revised-4/25/10

  30. On a phase diagram, the triple point is the set of P and T where all three phases can coexist in equilibrium. Sublimation is the process by which a solid transitions into a gas (and gas  solid). Ch14c-Heat-Revised-4/25/10

  31. The critical point marks the end of the vapor pressure curve. A path around this point (i.e. the path does not cross the curve) does not result in a phase transition. Past the critical point it is not possible to distinguish between the liquid and gas phases. Ch14c-Heat-Revised-4/25/10

  32. Isotherms of a Pure Substance Ch14c-Heat-Revised-4/25/10

  33. P-V-T Surface for Helium Region described by Boyle’s Law Ch14c-Heat-Revised-4/25/10

  34. The top surface is characteristic of water while the surface on the bottom is characteristic of most other substances. Ch14c-Heat-Revised-4/25/10

  35. The Very Complex P-V-T Surface for Water Ch14c-Heat-Revised-4/25/10

  36. Thermal Conduction Through direct contact, heat can be conducted from regions of high temperature to regions of low temperature. Energy is transferred by collisions between neighboring atoms or molecules. Ch14c-Heat-Revised-4/25/10

  37. The Heat Transfer Equation The rate of energy transfer by conduction is where: Q is the heat flow (Joules), t is the time for which the heat flows (sec),  is the thermal conductivity (W/m-K), A is the cross-sectional area (m2), and T/d is the temperature gradient (oC/m). Ch14c-Heat-Revised-4/25/10

  38. Substances that are good conductors of Electricity are also good conductors of heat. Ch14c-Heat-Revised-4/25/10

  39. Glass Thermos Container The glass container is itself a poor conductor of heat and it is then covered with a layer of insulation. The glass is constructed as a double walled container with the air evacuated from the space between the walls. In addition, the inside surfaces of the glass, facing each other, are silvered to reduce the heat transfer due to radiation. Ch14c-Heat-Revised-4/25/10

  40. Thermal Resistance Also where R is the thermal resistance. This is convenient when heat is conducted through multiple layers (with a common area (A)), because the heat flowing through each layer is the same - limited by the poorest conductor. Ch14c-Heat-Revised-4/25/10

  41. R Factors Related to the thermal resistance (R) is the R-Factor where the R-Factor is given by. Ch14c-Heat-Revised-4/25/10

  42. R Factors for Various Materials Ch14c-Heat-Revised-4/25/10

  43. Example (text problem 14.48): A metal rod with a diameter of 2.30 cm and a length of 1.10 m has one end immersed in ice at 0 C and the other end in boiling water at 100 C. Assume no heat loss to the surrounding air. If the ice melts at a rate of 1.32 grams every 175 s, what is the thermal conductivity of the metal? Heat is conducted to the ice at a rate of The heat conducted to the ice in a time period t is The heat needed to melt a given mass of ice is Ch14c-Heat-Revised-4/25/10

  44. Example continued: Since all the heat conducted by the rod is absorbed by the ice, Ch14c-Heat-Revised-4/25/10

  45. Example (text problem 14.51): For a temperature difference of 20 C, one slab of material conducts 10.0 W/m2; another of the same shape conducts 20.0 W/m2. What is the rate of heat flow per m2 of surface when the slabs are placed side by side with a total temperature difference of 20 C? For each slab, the thermal resistance per square meter is Ch14c-Heat-Revised-4/25/10

  46. Example continued: When the materials are placed in series, the rate of heat flow is Ch14c-Heat-Revised-4/25/10

  47. Multiple Layers of Material In the steady state the same quantity of heat flows through both layers. The amount of het that flows through is determined by the properties of the poorer conductor. Ch14c-Heat-Revised-4/25/10

  48. Problems with Multiple Layers of Material Ch14c-Heat-Revised-4/25/10

  49. Thermal Convection Convection is the movement of heat by fluid (liquid or gas) currents. Material is transported from one place to another. Ch14c-Heat-Revised-4/25/10

  50. Examples of Thermal Convection Ch14c-Heat-Revised-4/25/10

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