Transcript Chapter 12
Heat and Temperature A thermal infrared image of a ball before (left) and after (right) being bounced. DEFINITION OF HEAT Heat is thermal energy that flows from a highertemperature object to a lower-temperature object because of a difference in temperatures. SI Unit of Heat: joule (J) or calories (cal) 4.184 J = 1 cal 4184 J = 1 Cal = 1 kcal What is the difference between a hot cup of coffee and a cold cup of water? In a hot cup of coffee there is more activity – the atoms are jiggling around more. We say that they have more kinetic energy. We might even say that they have more thermal energy (energy of random motion) or more internal energy because more energy is internal to the system. Which has more internal energy, a cup of hot water or an iceberg? The iceberg because it has more molecules jiggling The heat that flows from hot to cold originates in the internal energy of the hot substance. It is not correct to say that a substance contains heat. Internal energy is the total energy that the molecules possess (kinetic plus potential). Kinetic energy can be translational and rotational. Molecules have potential energy because of intermolecular forces. When we heat a substance, we increase Its internal energy. Temperature is related to the internal energy per molecule or the average kinetic energy of translational motion of molecules. Why do we give sparklers that burn at 12000C to kids ? There are not many combustible molecules in the sparkler so not much total energy – certainly below the kids threshold of feeling…so Although the temperature is high, (the amount of internal energy per molecule), the total internal energy is low! Measuring Temperature Thermometers use liquids that expand or contract easily with temperature. The liquid absorbs or transfers thermal energy. We say that a thermometer “measures its own temperature”… because any two things put together will come to the same temperature. When this happens, the thermometer and its environment are said to be in thermal equilibrium. A poorly constructed thermometer thus has the ability to change the temperature of its surroundings by absorbing too much heat. Scales of Temperature Temperatures are reported in degrees Celsius, degrees Fahrenheit or degrees Kelvin. 0 K is the temperature at which an ideal gas can theoretically be compressed to zero volume (called absolute zero) Kelvin temperatures are always positive so can be related proportionally to the average kinetic energy per molecule KEAv = 3/2 kT Scale Conversions There are 180 divisions on the 0F scale compared with 100 divisions on the oC scale so the scale factor is….. 180 / 100 = 9 / 5 because the 0F scale begins at 32 rather than 0 we must add this on, so….. TF = (9/5 TC) + 32.0 For the Kelvin scale, the freezing point of water is 273.15 K above absolute zero so.. TK = TC + 273.15 Temperature Practice 1. Normal body temperature is 98.6 0F. What is this on the Centigrade scale? TC = 5/9 (TF – 32) = 5/9 (98.6 – 32) = 370C 2. Room temperature is often taken to be 680F. What is this on the Centigrade and Kelvin scales? TC = 5/9 (TF – 32) = 5/9 (68 – 32) = 200C TK = TC + 273.15 = 20 + 273.15 = 293.15 K 3. The temperature of a filament in a light bulb is about 18000C. What is this on the Fahrenheit and Kelvin scales? TC = (9/5 TC ) + 32 = (9/5 1800) + 32) = 32720F TK = TC + 273.15 = 1800 + 273.15 = 2073 K Processes of Thermal Energy Transfer Conduction Conduction is the process by which kinetic energy is passed from molecule to molecule Metals have a lot of loose (free) electrons which can transmit vibrations (KE) quickly when high speed particles collide with slower moving ones. We say they are good heat conductors. All gasses (and most liquids) tend to be poor conductors. We say that they are good thermal insulators. Conduction Examples • Wooden or rubber handles on frying pans • Clothing worn in layers to trap air – a poor conductor • Wood or tiled floor feels cooler than carpet even though they are at the same temperature • Wood or tiled floor feels cooler than carpet even though they are at the same temperature • Snowflakes trap air in their crystals so are good insulators. Snow slows the escape of heat from the earth’s surface, so good for Eskimo dwellings and protection for animals from the cold. Processes of Thermal Energy Transfer Convection In convection, thermal energy moves between two points because of a bulk movement of matter When part of a fluid is heated, it tends to expand and thus its density is reduced. The colder fluid sinks and the hotter fluid rises up. This thermal infrared image shows hot oil boiling in a pan. The oil is transferring heat out of the pan by convection. Notice the hot (yellow) centers of rising hot oil and the cooler outlines of the sinking oil. Convection Examples • Central heating causes a room to warm up because a convection current is set up. The heat source should be near the ground. • Pilots of gliders (and many birds) use naturally occurring convection currents to stay above the ground • Sea breezes (winds) are often due to convection. During the day the land is hotter than the sea. Hot air rises from the land and there is a breeze onto the shore. During the night the situation is reversed. • A refrigerator cooling coil is placed at the top of the unit so that colder air sinks downwards and the warmer air is displaced upwards and cooled by the coil thus establishing a convection current. Processes of Thermal Energy Transfer Radiation Radiation is the process in which energy is transferred by means of electromagnetic waves. For most everyday objects, this radiation is in the infra-red part of the electromagnetic spectrum. The source of EM waves is vibrating electrons in matter A thermal infrared image of the center of our galaxy. This heat from numerous stars and interstellar clouds traveled about 24,000 light years (about 150,000,000,000,000,000 miles!) through space by radiation to reach the infrared telescope Points to note: • An object at constant temperature will both absorb and radiate energy at the same rate. • A surface that is a good radiator is also a good absorber. • Surfaces that are light in color and smooth (shiny) are poor radiators (and poor absorbers). The reverse is true for dark and rough surfaces. • If the temperature of an object is increased then the frequency of the radiation increases. The total rate at which the energy is radiated will also increase. • Radiation can travel through a vacuum (space) Radiation Examples • The sun warms the Earth’s surface by radiation (principally short wavelength/high frequency IR) • The earth re-radiates energy back as low frequency radiation because the earth’s temperature is so low. The atmosphere is transparent to visible (high f) light but longer wavelengths are absorbed and reradiated back to earth especially by excess carbon dioxide and water vapor leading to increased global warming. • People wear light colored clothing in summer as it tends to not absorb the radiation from the sun. • A Halogen cook top uses several quartz-iodine lamps underneath a ceramic top (low conductivity). The EM radiation passes through the ceramic top and is absorbed by the bottom of the pot. • Thermos flask has silvered inside surface to reduce radiation. Heat and Specific Heat A person puts a pan on a stove heating ring and returns a few seconds later to find that the pan is hot. The same person puts a pan of water on the stove ring and returns minutes later to find that the pan is warm but far from hot. What does this tell you? Some substances will absorb a lot of heat for only a small change in temperature. Iron with a little heat will shoot up in temperature while water takes a lot of heat energy to make the temperature higher. Why is this? Heat and Specific Heat Temperature has a lot to do with the translational back and forth motion of atoms or molecules Iron’s electrons move rapidly back and forth and the temperature goes up quickly But…water doesn’t just shake back and forth, the molecules pucker in and out storing the energy in internal rotational states (potential energy) and the hydrogen bonding sticks them together so they don’t shake as much, so the temperature is not driven up as much. We say that water stores an enormous capacity of heat for small temperature changes – This is called specific heat Heat and Specific Heat We can define the heat capacity, C, of an object as the energy required to raise its temperature by 1 K. This is different for different substances. C = Q / T units: J / K or J / 0C Specific heat capacity, c, is the energy required to raise a unit mass of a substance by 1 K. c = Q / (m T) units: J / kg K or J / kg 0C We say that water stores an enormous capacity of heat for small temperature changes – This is called specific heat Heat and Temperature Change: Specific Heat Capacity Heat and Specific Heat It turns out that water will absorb a whole calorie of heat energy per gram and only change temperature by 1 degree Celcius (centigrade) We can think of specific heat as “thermal inertia” because it signifies the resistance of a substance to a change in temperature. Q = m c t c = specific heat capacity (cal/g0C) m = mass of object cwater = 1 cal/g0C or 4.184 J/g0C or 4184 J/kg0C t = change in temperature Heat and Specific Heat How much energy does it take to raise the temperature of 1.5 liters of water by 200C? mwater = 1.5 L ( 1kg / 1L) = 1.5 kg T = 20oC cwater = 1000 cal/kg0C or 4184 J/kg0C Q = m c t Q = (1.5 kg) (1000 cal/kg0C) (200C) = 30 000 cal Q = (1.5 kg) (4184 J/kg0C) (200C) = 125 520 J = 130 000 J Heat and Specific Heat Some high temperature foods, you can eat comfortably when you take them out of the oven as they have a low specific heat capacity and therefore don’t hold much thermal energy but water filled foods like pie filling you can burn your mouth on as the high temperature food will hold a lot of energy. A hot water bottle contains boiling water that cools gradually during the night releasing a large amount of thermal energy. Countries surrounded by water (which has a high specific heat) are heated by the warm winds that have absorbed thermal energy from the ocean (cons of energy). The ocean cools gradually during the winter so maintains a constant source of heat energy. The water acts as a temperature moderator, absorbing energy from the air above in the summer and releasing it in the winter. Heat and Temperature Change: Specific Heat Capacity A Hot Jogger In a half-hour, a 65-kg jogger can generate 8.0x105J of heat. This heat is removed from the body by a variety of means, including the body’s own temperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase? Q m cT 5 8.0 10 J Q 3.5 C T mc 65 kg 3500 J kg C Heat and Temperature Change: Specific Heat Capacity CALORIMETRY If there is no heat loss to the surroundings, the heat lost by the hotter object equals the heat gained by the cooler ones. Heat and Temperature Change: Specific Heat Capacity Measuring the Specific Heat Capacity The calorimeter is made of 0.15 kg of aluminum and contains 0.20 kg of water. Initially, the water and cup have the same temperature of 18.0oC. A 0.040 kg mass of unknown material is heated to a temperature of 97.0oC and then added to the water. After thermal equilibrium is reached, the temperature of the water, the cup, and the material is 22.0oC. Ignoring the small amount of heat gained by the thermometer, find the specific heat capacity of the unknown material. Heat and Temperature Change: Specific Heat Capacity mcT Al mcT water mcT unknown mcT Al mcT water cunknown mT unknown 9.00 102 J kg C 0.15 kg 4.0 C 4186 J kg C 0.20 kg 4.0 C 0.040 kg 75.0 C 1300 J kg C Phase Changes Why do you feel cold when you get out of a pool and a breeze is blowing? Water evaporates off your body and cools you down. How come? Why is evaporation a cooling process? Molecules in a liquid have a distribution of speeds and the average relates to what we call Temperature. When faster moving molecules leave a liquid’s surface they leave behind the slower moving molecules, which lowers the average speed and therefore the temperature of the liquid. Normal distribution curves of molecular speeds for ideal gas at 100 K and 900 K respectively Phase Changes In hot climates, sacking is put over clay pots and kept wet. Why? Evaporation of water from the sack cools the sack and thus draws thermal energy outwards from the water inside the pot. This keeps the drinking water nice and cool. How do we keep cool? We perspire (sweat), so evaporation takes place from our skin’s surface. Why do dogs pant? (or other animals without sweat glands) They can’t sweat so they create a large surface area (tongue and bronchial tract) from which liquid can evaporate and therefore cool them down. Similarly rubbing your hands under a hand dryer creates a larger surface for water to evaporate. Phase Changes Evaporation depends upon the temperature of the liquid and air surrounding the liquid, the surface area of the liquid and the moisture content in the air (humidity). Evaporating molecules form a vapor above the liquid. Equilibrium is reached when the vapor pressure exerted on the fluids surface returns liquid molecules to the liquid at the same rate they leave. How do fans keep people cool? Lower vapor pressure so more evaporation so….more cooling Why are their warning signs on hot tubs about staying in too long? In a hot tub you sweat like mad but the water can’t evaporate off the skin so your body heats up and can be dangerous if you stay in too long. Name at least two ways to cool a hot cup of coffee? Increase evaporation by blowing on it, pouring it into a saucer Cool by conduction by pouring in cool saucer, adding ice cubes, stirring with cool silverware Phase Changes Is condensation a heating or a cooling process? It is a heating process. The slower moving water vapor molecules stick together (forming droplets) while the higher speed molecules remain in the gaseous state thus increasing the average KE of the air molecules and thus the temperature. Why do people dry off in a steamy bathroom? The cooling effect of water evaporating off their body is balanced by the heating effect of steam condensing on it. That is why my 4-year old daughter asks for the warm water to be left in the tub while she is drying off. Phase Changes If evaporation is a cooling process is boiling a heating process? Heating the water in a pan is a heating process but the act of boiling is actually a cooling process. Like evaporation, when boiling, molecules leave the surface of the liquid taking thermal energy with them. What influences the ability of a liquid to boil other than temperature? The air pressure acting on the liquid Heat pan of water, bubbles form but 30km of air pushing down (atmospheric pressure) squashes these bubbles. With more heating the temp keeps increasing and the molecules become more energetic until bubbles are able to withstand the pressure. This temps for water is 1000C at sea level. What happens to this process if you are up a mountain? Closer to top of air therefore less pressure so bubbles stay formed at a lower temperature. Phase Changes You normally cook eggs for 3 minutes at sea level. Do you cook them for a longer or shorter time when living at higher altitude? Longer as water boils at a lower temp If you heat water at atmospheric pressure it boils at 1000C but if you turn up the heat it doesn’t get any hotter, how come? The more you heat, the more vigorous the boiling but you also have more liquid escaping therefore more cooling so they offset each other. (you can also think of it as the heat input going towards breaking intermolecular bonds and not towards changing the average kinetic energy of the molecules). If you put a cover on a pan of spaghetti will it cook faster? Yes, the lid increases the pressure so temp goes up more before bubbles stay formed. Phase Changes Why are sensitive fruit crops in the South sprayed with water before a forecasted frost? Like condensation (gas to liquid), changing state from liquid to solid is also a heating process. The heat liberated in freezing the layer of water around the outside of the strawberry, actually protects the strawberry inside. Phase Changes In the past, farmers used to put a tub of water in the cellar where they stored their canned food. Why? If the temperature in the cellar dropped the water in the tub would freeze before the liquid in the cans (which had added salt or sugars) thus releasing heat and warming the room. Phase Changes Which will hurt more, a steam burn at 1000C or a water burn at 1000C ? The steam burn is much more serious because each gram of steam liberates 540 calories when it condenses, whereas water only liberates 1cal for every gram for every degree (or only 100 cal to go from 1000C to 0 0C). Note: When 540 cal is used to turn a gram of water into steam it does not go into increasing the molecules KE, so it must go into increasing their PE. Intermolecular bonds have to be broken and this takes a lot of energy. When steam condenses, bonds form and this energy is released. Phase Changes Why is an ice rink flooded with hot water to smooth out the ice? Wouldn’t cold water work better? Above 800C, hot water freezes faster than warm water. For a large surface area like an ice skating rink, the rate of cooling by rapid evaporation is very high because each gram of water that evaporates, draws at least 540 cals/gram from the water left behind. This is huge compared with the 1 cal/g/0C that is drawn for each gram of water that cools by thermal conduction. Role of heat transfer through evaporation and condensation in a refrigerator Phase Changes Latent Heat of Fusion: The quantity of heat needed per kg to melt a solid (or solidify a liquid) at constant temperature and atmospheric pressure. Change in heat = (mass)(heat of fusion) Q = m Lf Lf units: J/kg Lf,water = 80 cal/g or 3.35 x 105 J/kg Latent Heat of Vaporization: The quantity of heat needed per kg to vaporize a liquid (or liquefy a gas) at room temperature and atmospheric pressure. Change in heat = (mass)(heat of vaporization) Q = m Lv Lv units: J/kg Lv,water = 540 cal/g or 2.26 x 106 J/kg More than 6x’s Lf for water Phase Changes Latent Heat of Fusion: The quantity of heat needed per kg to melt a solid (or solidify a liquid) at constant temperature and atmospheric pressure. Change in heat = (mass)(heat of fusion) Q = m Lf Lf units: J/kg Lf,water = 80 cal/g or 3.35 x 105 J/kg Latent Heat of Vaporization: The quantity of heat needed per kg to vaporize a liquid (or liquefy a gas) at room temperature and atmospheric pressure. Change in heat = (mass)(heat of vaporization) Q = m Lv Lv units: J/kg Lv,water = 540 cal/g or 2.26 x 106 J/kg More than 6x’s Lf for water Gas Laws Robert Boyle (1627-1691) The volume of a gas is inversely proportional to the pressure applied when the temperature is kept constant. V 1/ P (constant T) PV = constant Kinetic Theory Interpretation The pressure exerted on the wall of a container is due to the constant bombardment of molecules. If the volume is reduced (say in half), the molecules will hit the walls at a faster rate because they have less distance to travel between collisions so in this case twice as many will be striking a given area of the wall per second, hence the pressure will be twice as great. Gas Laws Jacques Charles (1746 – 1823) When the pressure is not too high and is kept constant, the volume of a gas increases with temperature at a nearly constant rate. V T (constant P) V/T = constant Kinetic Theory Interpretation If you heat up a gas the molecules will move faster so to keep the number of collisions per second (with the container walls) the same, the volume must increase proportionally to the average speed so proportionally to the temperature. Gas Laws Joseph Gay-Lussac (1778 – 1850) At constant volume, the pressure of a gas is directly proportional to the absolute temperature. PT (constant T) P / T = constant Kinetic Theory Interpretation If you heat up a gas the molecules will move faster and if the volume stays the same there will be proportionally more collisions with each wall per second so the pressure will increase proportionally. Gas Laws Ideal Gas Law Looking at Boyle’s and Charles’s Law it can be seen that V T/P Comparing this expression with Gay-Lussac’s Law PV T We must also take into account the mass of gas (more mass, more change in momentum when gas hits walls which will exert more pressure, if volume and temp held constant) PV mT It turns out that the proportionality constant turns out to depend on the number of molecules that are in the gas – not their type so….. Gas Laws Ideal Gas Law Remember, to change a proportion into a equals sign you multiply the right hand side by a constant P in N/m2 = Pascals (Pa) V in m3 n = # moles of the gas = mass (grams) molecular mass PV = n R T T in K R = universal gas constant = 8.315 J/mol K For a certain amount of gas PV/T = nR = constant P1V1 / T1 = P2V2 / T2 Gas Laws Ideal Gas Law Note: A real gas does not follow this relationship precisely. At high pressure (and density) or when the gas is near the liquefaction point (boiling point). However at pressures on the order of 1 atm or less, and when T is not close to the liquefaction point of the gas it is quite accurate. Real gas behavior can be seen when volume of a gas is plotted against temp. Volume 0K Temperature (K) -273.15 0C Gasses liquefy at low temps so the line cannot extend below the liquefaction point. Nonetheless, the straight line projects back to –2730C (0K) for all gasses so the temp at which an ideal gas would have zero volume is called the absolute zero of temperature Gas Laws Examples 1. Determine the volume of 1 mole of any gas at STP assuming it behaves as an ideal gas. T = 273 K n = 1 mol V = nRT / P P = 1.00 atm = 1.013 x 105 N/m2 R = 8.315 J/mol K = (1 mol)(8.315 J/mol K)(273K) / (1.013 x 105 N/m2) V = 22.4 x 10-3 m3 = 22.4 L Gas Laws Examples 2. At a certain altitude the heating unit in a hot air balloon is tuned off and the balloon begins to cool and the balloon descends. Why do both the pressure and volume of the air within the balloon remain constant, even though the balloon’s air cools? The opening of the balloon allows air to escape, maintaining a constant pressure. Gas Laws Examples 3. A pressure cooker is used to cook food faster. Water will normally boil at a temperature of 373 K and an atmosphere pressure of 1.01 x 105 Pa. What is the boiling temperature inside the pot when the pressure is increased to 1.28 x 105 Pa? P1 = 1.01 x 105 Pa P2 = 1.28 x 105 Pa T1 = 273 K V = constant T2 = ? P1V / T1 = P2V / T2 T2 = P2 T1 / P1 = 473 K = (1.28 x 105 Pa) (373 K) / (1.01 x 105 Pa) Gas Laws Examples 4. In a jet liner ascending from sea level where the cabin pressure starts off at 1.01 x 105 Pa to flying altitude where the cabin pressure drops slightly to 1.00 x 105 Pa despite pressurized conditions. A person will feel a strange sensation in their middle ear, whose volume is 6.0 x 10-7 m3. What is the new volume of air inside the person’s middle ear and what can they do to compensate for this change in volume? P1 = 1.01 x 105 Pa V1 = 6.0 x 10-7 m3 P2 = 1.00 x 105 Pa V2 = ? P1V / T1 = P2V / T2 V2 = P1 V1 / P2 = (1.01) (6.0 x 10-7 m3) / (1.00) = 6.1 x 10-7 m3 Swallowing or yawning clears the Eustachian tube by reducing the volume of air.