Heat and Internal Energy Internal Energy U is

Heat and Internal Energy • Internal Energy U is the total 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 the intermolecular potential energy – Does not include macroscopic kinetic energy or external potential energy • Heat refers to the transfer of energy between a system and its environment due to a temperature difference between them – Amount of energy transferred by heat designated by symbol Q – A system does not have heat, just like it does not have work (heat and work speak to transfer of energy)

Units of Heat • The historical unit of heat was the calorie – 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, with a capital C) is 1000 cal • Since heat (like work) is a measure of energy transfer, its SI unit is the joule – 1 cal = 4. 186 J (“Mechanical Equivalent of Heat”) – New definition of the calorie • The unit of heat in the U. S. customary system is the British thermal unit (BTU) – Defined as the amount of energy necessary to raise the temperature of 1 lb of water from 63°F to 64°F

More About Heat • Heat is a microscopic form of energy transfer involving large numbers of particles • Energy exchange occurs due to individual interactions of the particles – No macroscopic displacements or forces involved • Heat flow is from a system at higher temperature to one at lower temperature – Flow of heat tends to equalize average microscopic kinetic energy of molecules • When 2 systems are in thermal equilibrium, they are at the same temperature and there is no net heat flow • Energy transferred by heat does not always mean there is a temperature change (see phase changes)

Heat Transfer Simulation presented in class. (Activ. Physics Online Exercise #8. 6, copyright Addison Wesley publishing)

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, defined as: (units of J / kg o. C) • Or – DT is always the final temperature minus the initial temperature – When the temperature increases, DT and Q are considered to be positive and energy flows into the system – When the temperature decreases, DT and Q are considered to be negative and energy flows out of the system – c varies slightly with temperature

Consequences of Different Specific Heats • Air circulation at the beach – 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, creating air circulation pattern • Moderate winter temperatures in regions near large bodies of water – Water transfers energy to air, which carries energy toward land (predominant on west coast rather than east coast) • Similar effect creates thermals (rising layers of air) which help flight of eagles and hang gliders – Sections of land are at higher temp. than other areas

Calorimetry • Calorimetry means “measuring heat” – In practice, it is a technique used to measure specific heat • Technique involves: – Raising temperature of object(s) to some value – Place object(s) in vessel containing cold water of known mass and temperature – Measure temperature of object(s) + water after equilibrium is reached • A calorimeter is a vessel providing good insulation that allows a thermal equilibrium to be achieved between substances without any energy loss to the environment (styrofoam cup or thermos with lid) • Conservation of energy requires that: (Q > 0 (< 0) when energy is gained (lost))

Example Problem #11. 17 An aluminum cup contains 225 g of water and a 40 -g copper stirrer, all at 27°C. A 400 -g sample of silver at an initial temperature of 87°C is placed in the water. The stirrer is used to stir the mixture until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup. Solution (details given in class): 80 g

CQ 1: Interactive Example Problem: Calorimetry Part (a): What is the energy released via heat by the block? A) B) C) D) E) 193 J – 193 J 193 k. J – 193 k. J 4186 k. J (Physlet Physics Exploration #19. 3, copyright Prentice–Hall publishing)

CQ 2: Interactive Example Problem: Calorimetry Part (c): What is the equilibrium temperature of the system? A) B) C) D) E) 300. 0 K 304. 6 K 319. 0 K 327. 1 K 1000 K (Physlet Physics Exploration #19. 3, copyright Prentice–Hall publishing)

Phase Transitions • A phase transition occurs when the physical characteristics of the substance change from one form to another • Common phase transitions are – Solid liquid (melting) – Liquid gas (boiling) • Phase transitions involve a change in the internal energy, but no change in temperature – Kinetic energy of molecules (which is related to temperature) is not changing, but their potential energy changes as work is done to change their positions • Energy required to change the phase of a given mass m of a pure substance is: – L = latent heat – depends on substance and nature of phase transition – + (–) sign used if energy is added (removed)

Phase Transitions • All phase changes can go in either direction – Heat flowing into a substance can cause melting (solid to liquid) or boiling (liquid to gas) – Heat flowing out of a substance can cause freezing (liquid to solid) or condensation (gas to liquid) • Latent heat of fusion Lf is used for melting or freezing • Latent heat of vaporization Lv is used for boiling or condensing (somewhat larger for lower pressures) • Table 11. 2 gives the latent heats for various substances • Large Lf of water is partly why spraying fruit trees with water can protect the buds from freezing – In process of freezing, water gives up a large amount of energy and keeps bud temperature from going below 0°C

T vs. Q for Transition from Ice to Steam Initial state: 1 g of ice at – 30°C Final state: 1 g of steam at 120°C Qtot = 3. 11 103 J • Part A: Temperature of ice changes from – 30°C to 0°C – Q = mcice DT = (1. 00 10– 3 kg)(2090 J/kg °C)(30. 0°C) = 62. 7 J • Part B: Ice melts to water at 0°C – Q = m. Lf = (1. 00 10– 3 kg)(3. 33 105 J/kg) = 333 J • Part C: Temperature of water changes from 0°C to 100°C – Q = mcwater DT = (1. 00 10– 3 kg)(4. 19 103 J/kg °C)(100°C) = 419 J • Part D: Water changes to steam at 100°C – Q = m. Lv = (1. 00 10– 3 kg)(2. 26 106 J/kg) = 2. 26 103 J • Part E: Temperature of steam changes from 100°C to 120°C – Q = mcsteam DT = (1. 00 10– 3 kg)(2. 01 103 J/kg °C)(20°C) = 40. 2 J

Evaporation and Condensation • The previous example shows why a burn caused by 100°C steam is much more severe than a burn caused by 100°C water – Steam releases large amount of energy through heat as it condenses to form water on the skin – Much more energy is transferred to the skin than would be the case for same amount of water at 100°C • Evaporation is similar to boiling – Molecular bonds are being broken by the most energetic molecules – Average kinetic energy is lowered as a result, which is why evaporation is a cooling process – Approximately the same latent heat of vaporization applies – Reason why you feel cool after stepping out from a swimming pool

Example Problem #11. 31 A 40 -g block of ice is cooled to – 78°C and is then added to 560 g of water in an 80 -g copper calorimeter at a temperature of 25°C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left. ) Remember that the ice must first warm to 0°C, melt, and then continue warming as water. The specific heat of ice is 0. 500 cal/g °C = 2090 J/kg °C. Solution (details given in class): 16°C

Conduction • Energy can be transferred via heat in one of three ways: conduction, convection, radiation • Conduction occurs with temperature differences • Transfer by conduction can be understood 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 – Net result is heat flow from higher temperature region to lower temperature region • Rate of conduction depends upon the characteristics of the substance – Metals are good conductors due to loosely-bound electrons

Conduction • Consider the flow of heat by conduction through a slab of crosssectional area A and width L • The rate of energy transfer (power) is given by: L – Assumes that slab is insulated so that energy cannot escape by conduction from its surface except at the ends – k is thermal conductivity and depends on the material – Substances that are good (poor) conductors have large (small) thermal conductivities (see Table 11. 3) – P is in Watts when Q is in Joules and Dt is in seconds

Home Insulation • In engineering, the insulating quality of materials are rated according to their R value: R = L / k • R values have strange units: °F ft 2 / (Btu/h) – That’s why units are not usually given! • Substances with larger R value are better insulators • For multiple layers, the total R value is the sum of the R values of each layer • Still air provides good insulation, but moving air increases the energy loss by conduction in a home – Much of thermal resistance of a window is due to the stagnant air layers rather than to the glass

Convection • Convection is heat flow by the movement of a fluid • When the movement results from differences in density, it is called natural convection (fluid currents are due to gravity) – Air currents at the beach – Water currents in a saucepan while heating • When the movement is forced by a fan or a pump, it is called forced convection (fluid is pushed around by mechanical means – fan or pump) – Forced-air heating systems – Hot-water baseboard heating – Blood circulation in the body (although air currents move under natural convection)

Thermal Radiation • Thermal radiation transfers energy through emission of electromagnetic waves – does not require physical contact • All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules – At ordinary temperatures (~20°C) nearly all the radiation is in the infrared (wavelengths longer than visible light) – At 800°C a body emits enough visible radiation to be selfluminous and appears “red-hot” – At 3000°C (incandescent lamp filament) the radiation contains enough visible light so the body appears “whitehot” • An ideal emitter and absorber of radiation is called a blackbody (would appear black)

Thermal Radiation • The rate at which energy is radiated is given by Stefan’s Law: – – P is the rate of energy transfer (power), in Watts σ = Stefan-Boltzmann constant = 5. 6696 x 10– 8 W/m 2 K 4 A is the surface area of the object e is a constant called the emissivity, and ranges from 0 to 1 depending on the properties of the object’s surface – T is the temperature in Kelvin • Objects absorb radiation as well • Net rate of energy gained or lost given by: – T 0 = temperature of environment

Applications of Thermal Radiation • Choice of clothing – Black fabric acts as a good absorber, so about half of the emitted energy radiates toward the body – White fabric reflects thermal radiation well • Thermography as medical diagnostic tool – Measurement of emitted thermal energy using infrared detectors, producing a visual display (see Fig. 11. 13) – Areas of high temperature are indicated, showing regions of abnormal cellular activity • Measuring body temperature – Radiation thermometer measures the intensity of the infrared radiation from the eardrum (see Fig. 11. 14) – Eardrum is good location to measure temperature since it is near hypothalamus (body’s temperature control center)

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 energy transfer by radiation • Neck size is reduced • Same principle behind dressing in coats and sweaters to keep warm – Warmer air is trapped close to our bodies, reducing energy loss by convection and conduction

Global Warming • Analogous to a greenhouse – Visible light and short-wavelength infrared radiation are absorbed by contents of greenhouse, resulting in the emission of longer-wavelength infrared radiation (IR) – Longer-wavelength IR absorbed by glass – Glass emits IR, half of which is emitted back inside the greenhouse – Convection currents are inhibited by the glass (although this is not mirrored in Earth’s atmosphere) • Earth’s atmosphere fills role of glass roof in greenhouse – “Greenhouse gasses” like CO 2 are particularly good absorbers of IR – More greenhouse gasses in the atmosphere means more IR is absorbed and Earth’s surface becomes warmer