# Chapter 11. Energy in Thermal Processes

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1 Chapter 11 Energy in Thermal Processes

2 Energy Transfer When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler increases The energy exchange ceases when the objects reach thermal equilibrium The concept of energy was broadened from just mechanical to include internal Made Conservation of Energy a universal law of nature

3 Heat Compared to Internal Energy Important to distinguish between them They are not interchangeable They mean very different things when used in physics

4 Internal Energy Internal Energy, U, is the energy associated with the microscopic components of the system Includes kinetic and potential energy associated with the random translational, rotational and vibrational motion of the atoms or molecules Also includes any potential energy bonding the particles together

5 Heat Heat is the transfer of energy between a system and its environment because of a temperature difference between them The symbol Q is used to represent the amount of energy transferred by heat between a system and its environment

6 Units of Heat Calorie An historical unit, before the connection between thermodynamics and mechanics was recognized A calorie is the amount of energy necessary to raise the temperature of 1 g of water from 14.5 C to 15.5 C. A Calorie (food calorie) is 1000 cal

7 Units of Heat, cont. US Customary Unit BTU BTU stands for British Thermal Unit A BTU is the amount of energy necessary to raise the temperature of 1 lb of water from 63 F to 64 F 1BTU = 1055 J 1 cal = J This is called the Mechanical Equivalent of Heat

8 James Prescott Joule British physicist Conservation of Energy Relationship between heat and other forms of energy transfer

9 Specific Heat Every substance requires a unique amount of energy per unit mass to change the temperature of that substance by 1 C The specific heat, c, of a substance is a measure of this amount c m Q T

10 Units of Specific Heat SI units J / kg C Historical units cal / g C

11 Heat and Specific Heat Q = m c T T is always the final temperature minus the initial temperature When the temperature increases, T and Q are considered to be positive and energy flows into the system When the temperature decreases, T and Q are considered to be negative and energy flows out of the system

12

13 Example 1 A steel strut is 2 m long, with a mass of 1.57 kg and cross-sectional area of 1x10-4 m 2. During the operation of the furnace the strut absorbs the net thermal energy of 2.5x10 5 J. Find the change in temperature of the strut. ( specific heat of steel is 448 J/kg oc)

14 Example 2 What is the temperature increase of 4.0 kg of water when heated by an 800-W immersion heater for 10 min? (c w = J/kg C)

15 Example 3 A solar heating system has a 25.0% conversion efficiency; the solar radiation incident on the panels is 800 W/m 2. What is the increase in temperature of 30.0 kg of water in a 1.00-h period by a 4.00-m 2 -area collector? (c w = J/kg C)

16 Example 4 A 2.00-kg copper rod is cm long at 23 C. If J are transferred to the rod by heat, what is its change in length? c copper = 387 J/kg C and copper = / C.

17 A Consequence of Different Specific Heats Water has a high specific heat compared to land On a hot day, the air above the land warms faster The warmer air flows upward and cooler air moves toward the beach

18 Calorimeter One technique for determining the specific heat of a substance A calorimeter is a vessel that is a good insulator which allows a thermal equilibrium to be achieved between substances without any energy loss to the environment

19 Calorimetry Analysis performed using a calorimeter Conservation of energy applies to the isolated system The energy that leaves the warmer substance equals the energy that enters the water Q cold = -Q hot Negative sign keeps consistency in the sign convention of T

20 Calorimetry with More Than Two Materials In some cases it may be difficult to determine which materials gain heat and which materials lose heat You can start with Q = 0 Each Q = m c T Use T f T i You don t have to determine before using the equation which materials will gain or lose heat

21 Example 5 A 125-g block of unknown substance with a temperature of 90 o C is placed in a Styrofoam cup containing kg of water at 20 0 C. The system reaches an equilibrium temperature of C. What is the specific heat of the substance, if the heat capacity of the cup is neglected?

22 Example 6 Find the final equilibrium temperature when 10.0 g of milk at 10.0 C is added to 160 g of coffee at 90.0 C. (Assume the specific heats of coffee and milk are the same as water and neglect the heat capacity of the container.) c water = 1.00 cal/g C = 4186 J/kg C

23 Problem Solving Hint It is important to organize the information in a problem A table will be helpful Headings can be Q material m c T f T i

24 Phase Changes A phase change occurs when the physical characteristics of the substance change from one form to another Common phases changes are Solid to liquid melting Liquid to gas boiling Phases changes involve a change in the internal energy, but no change in temperature

25 Latent Heat During a phase change, the amount of heat is given as Q = ±m L L is the latent heat of the substance Latent means hidden L depends on the substance and the nature of the phase change Choose a positive sign if you are adding energy to the system and a negative sign if energy is being removed from the system

26 Latent Heat, cont. SI units of latent heat are J / kg Latent heat of fusion, L f, is used for melting or freezing Latent heat of vaporization, L v, is used for boiling or condensing Table 11.2 gives the latent heats for various substances

27 Sublimation Some substances will go directly from solid to gaseous phase Without passing through the liquid phase This process is called sublimation There will be a latent heat of sublimation associated with this phase change

28

29 Graph of Ice to Steam

30 Warming Ice Start with one gram of ice at 30.0º C During A, the temperature of the ice changes from 30.0º C to 0º C Use Q = m c T Will add 62.7 J of energy

31 Melting Ice Once at 0º C, the phase change (melting) starts The temperature stays the same although energy is still being added Use Q = m L f Needs 333 J of energy

32 Example 7 Iced tea is made by adding ice to 1.8 kg of hot tea, initially at 80 C. How many kg of ice, initially at 0 C, are required to bring the mixture to 10 C? (L f = 3.33 x 10 5 J/kg, c w = J/kg C)

33 Warming Water Between 0º C and 100º C, the material is liquid and no phase changes take place Energy added increases the temperature Use Q = m c T 419 J of energy are added

34 Boiling Water At 100º C, a phase change occurs (boiling) Temperature does not change Use Q = m Lv J of energy are needed

35 Heating Steam After all the water is converted to steam, the steam will heat up No phase change occurs The added energy goes to increasing the temperature Use Q = m c T To raise the temperature of the steam to 120, 40.2 J of energy are needed

36 Problem Solving Strategies Make a table A column for each quantity A row for each phase and/or phase change Use a final column for the combination of quantities Use consistent units

37 Problem Solving Strategies, cont Apply Conservation of Energy Transfers in energy are given as Q=mc T for processes with no phase changes Use Q = m L f or Q = m L v if there is a phase change Start with Q = 0 Or Q cold = - Q hot, but be careful of sign T is T f T i Solve for the unknown

38 Methods of Heat Transfer Need to know the rate at which energy is transferred Need to know the mechanisms responsible for the transfer Methods include Conduction Convection Radiation

39 Conduction The transfer can be viewed on an atomic scale It is an exchange of energy between microscopic particles by collisions Less energetic particles gain energy during collisions with more energetic particles Rate of conduction depends upon the characteristics of the substance

40 Conduction example The molecules vibrate about their equilibrium positions Particles near the stove coil vibrate with larger amplitudes These collide with adjacent molecules and transfer some energy Eventually, the energy travels entirely through the pan and its handle

41 Conduction, cont. In general, metals are good conductors They contain large numbers of electrons that are relatively free to move through the metal They can transport energy from one region to another Conduction can occur only if there is a difference in temperature between two parts of the conducting medium

42 Conduction, equation The slab allows energy to transfer from the region of higher temperature to the region of lower temperature Q T ka h Tc t L

43 Conduction, equation explanation A is the cross-sectional area L = x is the thickness of the slab or the length of a rod P is in Watts when Q is in Joules and t is in seconds k is the thermal conductivity of the material See table 11.3 for some conductivities Good conductors have high k values and good insulators have low k values

44 Home Insulation Substances are rated by their R values R = L / k See table 11.4 for some R values For multiple layers, the total R value is the sum of the R values of each layer Wind increases the energy loss by conduction in a home

45 Conduction and Insulation with Multiple Materials Each portion will have a specific thickness and a specific thermal conductivity The rate of conduction through each portion is equal

46 Multiple Materials, cont. The rate through the multiple materials will be Q t A T T A T T L i Ri k i i h c h C i T H and T C are the temperatures at the outer extremities of the compound material

47

48 Example 8 A wall of a house consists of a layer of 10.2 cm- thick layer of brick, a layer of fiber glass insulation 8.9 cm thick and a 1.25-cm-thick drywall. If inside the house the temperature is 23 0 C and the outside temperature is 0 0 C, determine the rate of energy transfer through 1m 2 of the wall. ( k brick =0.84 J/s m K, k insul = J/s m K, k drywall = 0.48 J/s m K, )

49 Example 9 A thermopane window consists of two glass panes, each 0.05 m thick, with a 1- cm-thick sealed layer of air in between. If inside the room temperature is 23 0 C and the outside temperature is 0 0 C, determine the rate of energy transfer through 1m 2 of the window. ( k glass =0.84 J/smK k air = J/smK )

50 Convection Energy transferred by the movement of a substance When the movement results from differences in density, it is called natural conduction When the movement is forced by a fan or a pump, it is called forced convection

51 Convection example Air directly above the flame is warmed and expands The density of the air decreases, and it rises The mass of air warms the hand as it moves by

52 Example 10 A Styrofoam box has a surface of 0.72 m 2 and a wall thickness of 7.4 cm. The temperature of the inner surface is C, and of the outside 36 0 C. If it takes 4 hours for 6 kg of ice to melt in the container, find the thermal conductivity of the Styrofoam. Answer: k = 0.41J/sKm

53 Convection applications Boiling water Radiators Upwelling Cooling automobile engines Algal blooms in ponds and lakes

54 Convection Current Example The radiator warms the air in the lower region of the room The warm air is less dense, so it rises to the ceiling The denser, cooler air sinks A continuous air current pattern is set up as shown

55 Radiation Radiation does not require physical contact All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules Rate of radiation is given by Stefan s Law

56 Radiation example The electromagnetic waves carry the energy from the fire to the hands No physical contact is necessary Cannot be accounted for by conduction or convection

57 Radiation equation = AeT 4 The power is the rate of energy transfer, in Watts σ = x 10-8 W/m 2. K 4 A is the surface area of the object e is a constant called the emissivity e varies from 0 to 1 T is the temperature in Kelvins

58 Energy Absorption and Emission by Radiation With its surroundings, the rate at which the object at temperature T with surroundings at T o radiates is net = Ae T T 4 4 o When an object is in equilibrium with its surroundings, it radiates and absorbs at the same rate Its temperature will not change

59 Example 10 A radiator has an emissivity of 0.8 and its exposed area is 1.3 m 2. The temperature of the radiator is 85 0 C and the surrounding temperature is 20 0 C. What is the net heat flow rate due to radiation from the radiator? σ = x 10-8 W/m 2. K 4

60 Ideal Absorbers An ideal absorber is defined as an object that absorbs all of the energy incident on it e = 1 This type of object is called a black body An ideal absorber is also an ideal radiator of energy

61 Ideal Reflector An ideal reflector absorbs none of the energy incident on it e = 0

62 Applications of Radiation Clothing Black fabric acts as a good absorber White fabric is a better reflector Thermography The amount of energy radiated by an object can be measured with a thermograph Body temperature Radiation thermometer measures the intensity of the infrared radiation from the eardrum

63 Resisting Energy Transfer Dewar flask/thermos bottle Designed to minimize energy transfer to surroundings Space between walls is evacuated to minimize conduction and convection Silvered surface minimizes radiation Neck size is reduced

64 Global Warming Greenhouse example Visible light is absorbed and reemitted as infrared radiation Convection currents are inhibited by the glass Earth s atmosphere is also a good transmitter of visible light and a good absorber of infrared radiation

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