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Question An ice cube is removed from the freezer and put in a cup of hot chocolate. Which statement is most accurate? A)Cold flows from the ice cube into the hot chocolate. B)Heat flows from the hot chocolate into the ice cube. C)The cold from the ice cube mixes with the heat from the hot chocolate.

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Question If the kinetic energy of an average ideal gas molecule in a sample at 20ºC doubles, its final temperature must be _______. A)10ºC B)40ºC C)313ºC D)none of the above

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Heat and Heat Transfer Where would you rather go for break, Montreal or Southern France?

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Heat Capacity Why do you burn your mouth (but not your hand) when you eat hot pie or pizza?

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Why do we go to the beach to cool off? All because water has a high heat capacity!

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Which heats up more quickly? Put a pot of water on the stove ~ 15 minutes to boil Put same mass of iron ~ 2 minutes to reach 100 o C Substances have different ability to absorb or lose heat.

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8 Heat Capacity and Specific Heat For many substances, under normal circumstances T Q. Example: heat pot of water Or Q = C T where C is the heat capacity. Takes more Q to boil 2 cups than 1 cup The specific heat capacity, or just specific heat, of a substance is the heat capacity per unit mass. or

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Which has a higher specific heat iron or water? A) Iron B) water Which has a higher specific heat water or sand? A) water B) sand

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Water has a very high specific heat

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12 Example (text problem 14.12): If 125.6 kJ of heat are supplied to 5.00 10 2 g of water at 22 C, what is the final temperature of the water?

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Example (text problem 14.19): A 0.400 kg aluminum teakettle 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?

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14 Example (text problem 14.19): A 0.400 kg aluminum teakettle 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 T f is The heat needed to raise the temperature of the aluminum to T f is Then Q total = Q w + Q Al = 732 kJ.

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15 Can we predict any specific heats? 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

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16 Define the molar specific heat at constant volume; 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, all the heat goes into increasing the average kinetic energy of the particles.

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17 The amount of added heat is If the gas is diatomic:

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18 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:

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Example (text problem 14.26): A container of nitrogen gas (N 2 ) 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? T 1 = 23 V 1 = 425 L P 1 = 3.5 atm Q = 26.6 T 2 = ? Change to standard units Absolute T, V in m 3 and P in N/m 2 T =296 o K V = 425 x 10 -3 m 3 P = 3.5 x 1.01 x10 5 N/m 2

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20 Example (text problem 14.26): A container of nitrogen gas (N 2 ) 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

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21 The change in temperature is The final temperature of the gas is T f = T i + T = 317 K = 44 C.

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23 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.

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24 The rate of energy transfer by conduction is where is the thermal conductivity, A is the cross- sectional area, and T/d is the temperature gradient, the temperature change per unit distance. depends on the material. Some materials conduct heat better than others

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25 where R is the thermal resistance. Also This is convenient when heat is conducted through multiple layers because

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26 Example (text problem 14.51): For a temperature difference of 20 C, one slab of material conducts 10.0 W/m 2 ; another of the same shape conducts 20.0 W/m 2. What is the rate of heat flow per m 2 of surface when the slabs are placed side by side with a total temperature difference of 20 C? For each slab, calculate the thermal resistance per square meter

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27 Example continued: When the materials are placed in series, When the materials are placed in series, the rate of heat flow is

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Final Exam IV just like all exams. Covers all material since Thanksgiving including material covered only in lecture. Final-Separate exam. Comprehensive, all material until Thanksgiving. 8 MC + 3 problems. Only from text material Recommend studying: HW most important +…. Curve exams and many lab grades + Promod’s lab – (3-5%) I am in my office T&W 2-5

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Question You are making macaroni and cheese for dinner, again. Which is the best choice for stirring the noodles in the pot of boiling water? A)a wooden spoon B)a metal spoon C)any kind of spoon D)your finger, but really fast

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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. If the ice melts at a rate of 1.32 grams every 175 s, what is the thermal conductivity of the metal? Assume no heat loss to the surrounding air.

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We are given geometrical information, A and d ∆T Rate of ice melting which is related to rate of heat transfer Find κ

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32 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. If the ice melts at a rate of 1.32 grams every 175 s, what is the thermal conductivity of the metal? Assume no heat loss to the surrounding air. Heat is conducted to the ice at a rate of Q c is the heat necessary to melt the ice. The heat needed to melt a given mass of ice is L f = 333 x 10 3 J/kg The heat conducted to the ice in a time period t is

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33 Example continued: Since all the heat conducted by the rod is absorbed by the ice,

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Question You are trying to transfer heat from a hot reservoir to a cold reservoir. You have at your disposal an aluminum rod and a copper rod of the same size. Which should you choose to have the highest rate of energy transfer? A)The copper rod alone B)The aluminum rod only C)The rods in parallel. D)The rods in series.

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Question You are in the doctor's office and notice that the metal instrument tray feels much colder than the exam table you are sitting on. This is because A)the tray actually is colder than the table. B)the exam table has a cushion inside, which is a good insulator. C)the metal conducts heat away from your hand more quickly than does the table.

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36 Thermal Convection Convection is the movement of heat by fluid currents. Material is transported from one place to another. Hot air rises. We can see the ripples in the air above a hot road. The rising air transfers heat.

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Convection can set up convection cells. Hot fluids rise and cool fluids sink. Important for cooking, weather, Sun, Ocean currents etc

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Fig. 14.12

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Fig. 14.16

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43 Thermal Radiation The most important source of heat on Earth is the Sun. How can the heat get here? There is nothing (vacuum between us and Sun) Not by conduction or convection. Heat gets here by radiation

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Radiation is a an electromagnetic (EM) wave. Light is one example of EM radiation Even if I turn out the lights this room is full of EM radiation

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Examples of radiation All bodies emit electromagnetic (EM) radiation. The perfect absorber and emitter of EM radiation is called a blackbody. The amount and type of radiation emitted depends on the temperature of the object.

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Why do we call them blackbodies?

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Question A wood-burning fireplace has a chimney which allows the heated air to rise and escape the house. How then does a fireplace then heat the room? A)convection B)conduction C)radiation D)all of the above

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48 The rate of energy emission by a blackbody is (Stefan’s Law) where A is the surface area of the emitting body, T is its temperature, and = 5.670 10 8 W/m 2 K 4 is the Stefan-Boltzmann constant.

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49 Since an ideal blackbody does not exist, Stefan’s law is written as where e is the emissivity; e = 0 for a perfect reflector of EM radiation and e = 1 for perfect blackbody.

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50 A spectrum shows the amount of radiation emitted at a particular wavelength. For a blackbody, the peak of the spectrum is determined only by its temperature. Wien’s law

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51 The net energy gained or lost by a blackbody at a temperature T is where T s is the temperature of the surroundings.

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52 Example (R&S 14): A sphere with a diameter of 80 cm is held at a temperature of 250 C and is radiating energy. If the intensity of the radiation detected at a distance of 2.0 m from the sphere’s center is 102 W/m 2, what is the emissivity of the sphere? The power emitted by a point source is This is the total power passing through a sphere of radius d The emissivity is Notice absolute T

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Thermos bottle and heat transfer Vacuum Silvered surface

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Thermos and heat transfer No Heat transfer by conduction. (Vacuum doesn’t conduct). Small losses through stopper. No convection (Vacuum) No heat transfer by radiation Silvered surface reflects heat radiation back into bottle

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Question Which of the following do not emit radiant energy? A) Sun B) Earth C) Cup of hot chocolate D) Ice cube E) all of the above emit radiation

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Good luck on all your finals! Especially Physics

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