VIEWS: 135 PAGES: 38 POSTED ON: 4/22/2011
***Heat equivalent… Heat and modern technology are inseparable One of the first to demonstrate that heat is a form of energy was James Prescott Joule (1818-1889) Thermal energy is a form of kinetic energy The good, the bad, and the ugly units of heat The SI unit of temperature is the Kelvin Is there an upper limit? Is there a lower limit? The driver of a 20,000-kg truck applies the brakes on a 10° downhill run in order to maintain speed. What is the temperature increase of 100 kg of brake material after the truck moves for 200 m? Assume an average specific heat of 800 J/kg·C° for the brake fluid. Q mgh 20,000 9.8 200 sin 10 T Q /(mc) 85 C How many stairs would you (75 kg) have to run to work off 500 Calories? mgh 500,000 4.18 h 2844 m # steps h / 0.2 14,218 Suppose a 65-kg person spends 8 hrs sleeping, 1 hr at moderate physical labor, 4 hrs in light activity, and 11 hrs working at a desk or relaxing. Is this person likely to gain weight if he maintains a 3500-Cal daily diet? Metabolic rates of an average 65-kg human activity Kcal/h watts Sleeping 60 70 Sitting upright 100 115 Light activity 200 230 (eating, dressing, household chores) Moderate work 400 460 (tennis, walking) Running (15 1000 1150 km/h) Bicycling (race) 1100 1270 (8·70+1·460+4·230+11·115)·3600=11.5 MJ=2800 Cal Consider the apparatus that Joule used in his experiments on the mechanical equivalent of heat. Suppose the block has a mass of 0.65 kg and that it falls through a distance of 0.55 m. Find the expected rise in temperature of the water given that 6200 J are needed for every 1.0°C increase. T mgh / 6200 5.7 10 4 C The 1.23 kg head of a hammer has a speed of 8.2 m/s just before it strikes a nail and is brought to rest. Estimate the temperature rise of a 13 g iron nail generated by twenty such hammer blows done in quick succession. Assume the nail absorbs all the energy. An iron meteorite melts when it enters the Earth's atmosphere. If its initial temperature, outside of the atmosphere, was -135°C, calculate the minimum velocity the meteorite must have had before it entered Earth's atmosphere. Water going over a waterfall drops through a height of about 62 m. Suppose that all the gravitational potential energy of the water goes into raising its temperature. Find the increase in water temperature at the bottom of the waterfall as compared with the top. Red blood in the tropics Robert Mayer (1814-1878) Joule’s paddlewheel experiment Heat Capacity… Specific Heat Capacities of Some Solids and Liquids Substance Specific Heat Capacity, c, J/(kg · C°)b Solids Aluminum 900 Copper 387 Glass (common) 840 Human body (37 °C, average) 3500 Ice (-15 °C) 2000 Iron or steel 452 Lead 128 Silver 235 Liquids Benzene 1740 Ethyl alcohol 2450 Glycerin 2410 Mercury 139 Water (15 °C) 4186 Of these three metals, aluminum needs the most heat per gram per degree when warmed, and releases the most heat when cooled. The temperature change depends on the amount of heat, on the amount of substance, and on the heat capacity. Which has the greater heat capacity, water or copper? How big is a Btu? 0.252 kcal = 1055 J Bomb calorimeter Bomb calorimetry lab Measuring the caloric value of food A certain calorimeter cup is made from 0.15 kg of aluminum and contains 0.20 kg of water. Initially, the water and the cup have a common temperature of 18.0 °C. A 0.040-kg mass of unknown material is heated to a temperature of 97.0 °C and then added to the water. The temperature of the water, the cup, and the unknown material is 22.0 °C after thermal equilibrium is reestablished. Ignoring the small amount of heat gained by the thermometer, find the specific heat capacity of the unknown material. A caring husband, upon finding his stove out of order, decides to boil the water for his wife's coffee by shaking it in a thermos flask. Suppose that he uses 430 cm3 of tap water at 15 °C, and that the water falls 1/3rd of a meter with each shake, at a rate of 20 per minute. Neglecting any loss of thermal energy by the flask, will his wife make to work on time? Q =m·4190·(100-15) = 153·m kJ W = 20·t·m·9.8·0.3 = 58.8·m·t Q = W or t = 2602 min = 43 hr In order to maintain constant weight, we must consume about 2000 kilocalories of food energy per day of inactivity. How long could you live off your fat? 30 4100 / 2000 61.5 days •1 pound of fat contains about 4100 kilocalories •On the average, 15%/22% of an adult male’s/female’s weight is in the form of body fat (assume about 30 lb) •In two days of starvation and inactivity, one would be able to lose about 1 lb of fat Most of the energy that we get from food goes into generating heat energy. How much will the temperature of a 75-kg man increase if he eats a cup of yogurt containing 350 kcal and does not release this energy to the environment? T = Q/mc = 350 kcal/(75 kg·0.83 kcal/kg·C°) = 5.6 C° Suppose Dee Zertz just finished indulging herself with 2 servings of cheese cake, worth about 500 Cal. If all “nutrients” in the cheese cake were immediately metabolized and no heat were lost to the environment, by how much would Dee’s body temperature rise? Assume Dee’s body contains 38 liters of water. 500,000 = 1000·38·∆T ∆T=13.2 °C Suppose 225 g of coffee at 80.3 °C and 12.2 g of cream at 5 °C are mixed in a ceramic cup, m=116 g and c=1.09 J/(g·C°), initially at room temperature (24 ºC). What is the equilibrium temperature of the mixture? (Assume that no heat is exchanged with the surroundings and that the specific heat of coffee and cream are roughly equal to that of water.) Does it matter which you pour in first? 225 4.18 (80.3 T ) 12.2 4.18 (T 5) 116 1.09 (T 24) T 70.5 C Consider a classroom containing 200 students. Assume that the metabolic rate of generating heat is 130 W for each student and that the heat accumulates during a 50-minute lecture. In addition, assume that the air has a molar specific heat of CV =(5/2)·R and that the room (volume = 1200 m3, initial pressure = 1.01 × 105 Pa, and initial temperature = 21 °C) is sealed shut. If all the heat generated by the students were absorbed by the air, by how much would the air temperature rise during a lecture? In a half-hour, a 65-kg jogger can generate 8.0 × 105 J of heat. This heat is removed from the jogger's 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? Cold water at a temperature of 15 °C enters a heater, and the resulting hot water has a temperature of 61 °C. If a person uses 120 kg of hot water in taking a shower, determine the cost of heating the water. Assume that the utility company charges $0.10 per kilowatt · hour for electrical energy. $$$ 6.4 0.10 64 c A 0.5-kg block of metal with an initial temperature of 30 °C is dropped into a container holding 1.12 kg of water at 20 °C. If the final temperature of the block-water system is 20.4 °C, what is the specific heat of the metal? (Assume no heat is exchanged with the container or environment.) End Burning money