Physics 2A (Fall 2012) Chapters 11:Using Energy and 12: Thermal Properties of Matter
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1 Physics 2A (Fall 2012) Chaters 11:Using Energy and 12: Thermal Proerties of Matter "Kee in mind that neither success nor failure is ever final." Roger Ward Babson Our greatest glory is not in never failing, but in rising u every time we fail. Ralh Waldo Emerson If you continue to do what you've always done, you'll continue to get what you've always got. Yogi Berra Defeat is not defeat unless acceted as a reality in your own mind. Bruce Lee Reading: sections , , , 12.8 Outline: transforming energy efficiency energy inuts energy oututs thermal energy and temerature Fahrenheit, Celsius, and Kelvin scales thermal energy atomic model of matter atomic mass and atomic mass number mole ideal gas rms seed ressure ideal gas law heat definition heat and temerature change heat and hase change calorimetry heat transfer conduction convection radiation
2 Problem Solving You should know the relationshis between the mass of a molecule, the mass of a mole of molecules, and the total mass of a collection of molecules. If a gas contains N molecules, each of mass m, the total mass is Nm. Since there are N A molecules in a mole, the gas contains N/N A moles. The molar mass M is the mass of N A molecules: M = N A m. If the gas contains n moles, its total mass is nm. Note that this is exactly the same as Nm. Many roblems require you to use the ideal gas law P = nrt to comute one of the quantities that aear in it. You should also know how to comute changes in one of the quantities for various rocesses. Heat (Q) is defined as energy that flows from a higher temerature object to a lower temerature object and is measured in units of joules. The energy Q absorbed or released as heat by a substance is related to the change in temerature ΔT by Q = mcδt, where c is the secific heat caacity. You should know how to calculate the final temerature of two or more objects, initially at different temeratures, when they have been in contact long enough to achieve thermal equilibrium. Use the condition that the energy released as heat by one object is absorbed as heat by the other. If the final temerature is known, this condition can be used to calculate the secific heat or mass of one of the objects. There are three mechanisms by which energy flows as heat from one lace to another: convection, conduction, and radiation. You should be able to differentiate between these three mechanisms and you should know the equations describing the conduction of heat through a material and the radiant heat emitted by an object. Questions and Examle Problems from Chaters 11 and 12 Question 1 Two identical mugs contain hot coffee from the same ot. One mug is full, while the other is only one-quarter full. Sitting on the kitchen table, which mug stays warmer longer? Exlain. Question 2 Your head feels colder under an air-conditioning vent when your hair is wet than when it is dry. Why? Question 3 Grandma says that it is quicker to bake a otato if you ut a nail into it. In fact, she is right. Justify her baking technique in terms of one of the three rocesses of heat transfer.
3 KNIG5491_02_ch11_ qxd 6/18/09 5:52 PM Page 349 Integrated Examle SUMMARY 349 The goals of Chater 11 have been to learn more about energy transformations and transfers, the laws of thermodynamics, and theoretical and ractical limitations on energy use. GENERAL PRINCIPLES Energy and Efficiency The Laws of Thermodynamics When energy is transformed from one form into another, some may be lost, usually to thermal energy, due to ractical or theoretical constraints. This limits the efficiency of rocesses. We define efficiency as what you get e= what you had to ay The first law of thermodynamics is a statement of conservation of energy for systems in which only thermal energy changes: Entroy and Irreversibility Systems move toward more robable states. These states have higher entroy more disorder. This change is irreversible. Changing other forms of energy to thermal energy is irreversible. E th = W + Q The second law of thermodynamics secifies the way that isolated systems can evolve: The entroy of an isolated system always increases. This law has ractical consequences: Heat energy sontaneously flows only from hot to cold. A transformation of energy into thermal energy is irreversible. No heat engine can be 100% efficient. Heat is energy transferred between Increasing robability Increasing entroy T2, T1 T1 two objects at different temeratures. Energy will be transferred until thermal equilibrium is reached. Q IMPORTANT CONCEPTS Thermal energy For a gas, the thermal energy is the total kinetic energy of motion of the atoms. Thermal energy is random kinetic energy and so has entroy. 3 E th = NK avg = Nk BT 2 Temerature For a gas, temerature is roortional to the average kinetic energy of the motion of the atoms. Two systems are in thermal equilibrium if they are at the same temerature. No heat energy is transferred at thermal equilibrium. A heat engine converts thermal energy from a hot reservoir into useful work. Some heat is exhausted into a cold reservoir, limiting efficiency. emax = 1 Hot reservoir 2 K avg T= 3 kb T1 A heat um uses an energy inut to transfer heat from a cold side to a hot side. The coefficient of erformance is analogous to efficiency. For cooling, it is: TC TH COPmax = Hot reservoir TH Heat engine Heat um Win Wout QC QC Cold reservoir TH QH QH T2 5 T1 TC TH - TC Cold reservoir TC TC APPLICATIONS Efficiencies Energy in the body Cells in the body metabolize chemical energy in food. Efficiency for most actions is about 25%. Power lants A tyical ower lant converts about 1/3 of the energy inut into useful work. The rest is exhausted as waste heat. Chemical energy in Energy used by body at rate of 480 W Waste heat Energy for forward roulsion at rate of 120 W Useful work out Temerature scales Zero on the Kelvin temerature scale is the temerature at which the kinetic energy of atoms is zero. This is absolute zero. The conversion from C to K is T(K) = T( C) All temeratures in equations must be in kelvin.
4 SUMMARY The goal of Chater 12 has been to use the atomic model of matter to exlain and exlore many macroscoic henomena associated with heat, temerature, and the roerties of matter. GENERAL PRINCIPLES Atomic Model We model matter as being made of simle basic articles. The relationshi of these articles to each other defines the hase. Gas Liquid Solid The atomic model exlains thermal exansion, secific heat, and heat transfer. Atomic Model of a Gas Macroscoic roerties of gases can be exlained in terms of the atomic model of the gas. The seed of the articles is related to the temerature: v rms = B 3k B T m The collisions of articles with each other and with the walls of the container determine the ressure.,, T Ideal-Gas Law The ideal gas law relates the ressure, volume, and temerature in a samle of gas. We can exress the law in terms of the number of atoms or the number of moles in the samle: = Nk B T = nrt For a gas rocess in a sealed container, i i T i = f f T f IMPORTANT CONCEPTS Effects of heat transfer A system that is heated can either change temerature or change hase. The secific heat c of a material is the Q = Mc T heat required to raise 1 kg by 1 K. The heat of transformation is the energy necessary to change the hase of 1 kg of a substance. Heat is added to change a solid to a liquid or a liquid to a gas; heat is removed to reverse these changes. The molar secific heat of a gas deends on the rocess. Q = e ML f (melt/freeze) ML v (boil/condense) For a constantvolume rocess: Q = nc c T For a constantressure rocess: Q = nc P T Mechanisms of heat transfer An object can transfer heat to other objects or to its environment: Conduction is the transfer of heat by direct hysical contact. Convection is the transfer of heat by the motion of a fluid. Radiation is the transfer of heat by electromagnetic waves. Q t = aka L b T Q t = esat 4 A (ressure-volume) diagram is a useful means of looking at a rocess involving a gas. A constant-volume rocess has no change in volume. An isobaric rocess haens at a constant ressure. An isothermal rocess haens at a constant temerature. An adiabatic rocess involves no transfer of heat; the temerature changes. The work done by a gas is the area under the grah. f i f i i i f f f i f f Isotherm i i f f Isotherms i f i i i f W 5 area i f APPLICATIONS Thermal exansion Objects exerience an increase in volume and an increase in length when their temerature changes: = b i T L = al i T Calorimetry When two or more systems interact thermally, they come to a common final temerature determined by Q net = Q 1 + Q 2 + Q 3 + Á = 0 The number of moles is M (in grams) n = M mol
5 Question 4 Assuming that air behaves like an ideal gas, exlain what haens to the ressure in a tightly sealed house when the electric furnace turns on for a while. Problem 1 A weightlifter works out at the gym each day. Part of her routine is to lie on her back and lift a 40 kg barbell straight u from chest height to full arm extension, a distance of 0.50 m. (a) How much work does the weightlifter do to lift the barbell one time? (b) If the weightlifter does 20 reetitions a day, what total energy does she exend on lifting, assuming a tyical efficiency for energy use by the body. (c) How many 400 Calorie donuts can she eat a day to suly that energy? Problem 2 A 10% efficient engine accelerates a 1500 kg car from rest to 15 m/s. How much energy is transferred to the engine by burning gasoline?
6 Problem 3 In an average human, basic life rocesses require energy to be sulied at a steady rate of 100 W. What daily energy in take, in Calories, is required to maintain these basic rocesses? Problem 4 An ideal gas is at 20 C. If we double the average kinetic energy of the gas atoms, what is the new temerature in C? Problem 5 How many atoms of hydrogen are in 100 g of hydrogen eroxide (H )?
7 Problem 6 Total lung caacity of a tyical adult is aroximately 5.0 L. Aroximately 20% of the air is oxygen. At sea level and at an average body temerature of 37 C, how many moles of oxygen do the lungs contain at the end of an inhalation? Problem 7 An ideal gas at 15.5 o C and a ressure of Pa occuies a volume of 2.81 m 3. (a) How many moles of gas are resent? (b) If the volume is raised to 4.16 m 3 and the temerature raised to 28.2 o C, what will be the ressure of the gas? Problem 8 A comressed-air tank holds m 3 of air at a temerature of 285 K and a ressure of 850 kpa. What volume would the air occuy if it were released into the atmoshere, where the ressure is 101 kpa and the temerature is 303 K.
8 Problem 9 What minimum heat is needed to bring 100 g of water at 20 o C to the boiling oint and comletely boil it away? Problem 10 A kg block of ice has a temerature of 10.0 o C. The block of ice then absorbs J of heat. What is the final hase (liquid or gas) and temerature?
9 Problem 11 When you take a bath, how many kilograms of hot water (49.0 o C) must you mix with cold water (13.0 o C) so that the temerature of the bath is 36.0 o C? The total mass of the water (hot lus cold) is 191 kg. Ignore any heat flow between the water and its external surroundings. Problem 12 Ideally, when a thermometer is used to measure the temerature of an object, the temerature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temerature will change. A thermometer has a mass of 31.0 g, a secific heat caacity of c = 815 J/(kg C o ), and a temerature of 12.0 o C. It is immersed in 119 g of water, and the final temerature of the water and thermometer is 41.5 o C. What was the temerature of the water before insertion of the thermometer?
10 Problem 13 A erson s body is roducing energy internally due to metabolic rocesses. If the body loses more energy that metabolic rocesses are generating, its temerature will dro. If the dro is severe, it can be life threatening. Suose a erson is unclothed and energy is being lost via radiation from a surface area of 1.40 m 2, which has a temerature of 34 o C and an emissivity of Suose that metabolic rocesses are roducing energy at a rate of 115 J/s. What is the temerature of the coldest room in which this erson could stand and not exerience a dro in body temerature? Problem 14 A erson s body is covered with 1.6 m 2 of wool clothing. The thickness of the wool is m. The temerature at the outside surface of the wool is 11 o C, and the skin temerature is 36 o C. How much heat er second does the erson lose due to conduction?
11 Problem 15 Suose the skin temerature of a naked erson is 34 o C when the erson is standing inside a room whose temerature is 25 o C. The skin area of the individual is 1.5 m 2. (a) Assuming the emissivity is 0.80, find the net loss of radiant ower from the body. (b) Determine the number of food Calories of energy (1 food Calorie = 4186 J) that is lost in one hour due to the net rate obtained in art (a). Metabolic conversion of food into energy relaces this loss.
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