Introduction to Chapter 26

Transcription

1 9 Heating and Cooling Introduction to Chapter 26 In this chapter, you will learn how heat and temperature are measured. Many people believe that heat and temperature are the same thing, but these two properties are different.temperature measures the average kinetic energy of a substance, whereas heat describes the flow of thermal energy from one substance to another. Chapter 26 Measuring Heat Investigations for Chapter Temperature Scales How is temperature measured? In this Investigation you will graph the Celsius temperature scale as a function of the Fahrenheit temperature scale. From this graph you will develop a mathematical relationship between the Fahrenheit and Celsius temperature scales Measuring Changes in Heat How efficient is an immersion heater? In this Investigation you will explore how much thermal energy is supplied to water by an immersion heater. You will also make some predictions on the change in temperature if the amount of water is changed. In addition, you will revisit the concept of efficiency to calculate the efficiency of the system Specific Heat How much heat flows between liquids at different temperatures? In this Investigation you will observe what happens to the final temperature when you mix hot and cold liquids. Next you will analyze how much heat flows from the hot liquid to the cold liquid. You will also determine the specific heat of alcohol. 441

2 : Measuring Heat Learning Goals In this chapter, you will: Measure temperature. Convert between the Celsius and Fahrenheit temperature scales. Understand and demonstrate physical changes due to temperature. Develop a mathematical relationship that describes how much the temperature of water increases when heat is added to the water. Discuss the relationship of heat and energy. Calculate the efficiency in a heating system. Predict the final temperature when two containers of water of different temperatures are mixed. Quantify the flow of heat from one container of water to another where there is an initial temperature difference between the two containers. Analyze temperature changes in terms of the flow of heat. Calculate the specific heat of a substance if a known quantity of that substance is mixed with water. Predict the equilibrium temperature of a mixture of water and another substance. Vocabulary British thermal unit (Btu) first law of thermodynamics latent heat thermal equilibrium calorie heat temperature thermometer Celsius scale heat-temperature rule thermal energy thermostat Fahrenheit scale 442

3 26.1 Temperature Scales You have probably used a thermometer. However, did you ever stop to think about how it works? In this section, you will learn how temperature is measured and how the devices we use to measure temperature work. Temperature What is temperature? What does temperature measure? If average kinetic energy increases, so does temperature Many people use a thermometer to find the temperature outside. Temperature is the measurement we use to quantify the sensations of hot and cold. A hot cup of coffee has a higher temperature than a cold glass of iced tea. But what does temperature actually measure? If we were to blow up a balloon we would fill it with billions upon billions of molecules of air. All of these molecules are constantly moving. If they are moving, they have kinetic energy. Some of the molecules are moving fast, some are moving slowly. They can move up, down, and sideways. Fast particles have more kinetic energy than slow particles. If we were to take the kinetic energy of every single molecule in a balloon, and divide it by the total number of molecules, we would have an average of the kinetic energy for molecules in the balloon. This average is what temperature measures. If we were to heat up a balloon, all of the molecules inside of it would start to move faster and faster. What does this tell you about the relationship between average kinetic energy and temperature? It tells you that increasing the temperature increases the random motion of the molecules, and so increases the average kinetic energy of the molecules. The temperature of an object measures the average kinetic energy of its molecules. Celsius scale The Celsius scale is also called the centigrade scale because the difference in temperature between the freezing and boiling points of water is divided into 100 degrees. Figure 26.1: As temperature increases, so does the average kinetic energy of the molecules.the sizes of the arrows in the balloons represent the amount of kinetic energy of the molecules they contain Temperature Scales 443

4 Temperature scales The Fahrenheit scale The Celsius scale The history of temperature scales You are probably most familiar with the English system of measuring temperature, known as the Fahrenheit scale. In the Fahrenheit scale, water freezes at 32 degrees (or 32 F) and water boils at 212 F. You have probably also taken your own body temperature, which is normally about 98.6 F. Room temperature is about 68 F. The SI, or metric, unit used to measure temperature is the degree centigrade, also known as the degree Celsius. In the Celsius scale, water freezes at zero degrees Celsius (or 0 C) and water boils at 100 C. Room temperature is about 25 C. Ole Roemer created the first commonly used temperature scale (the Roemer scale) in 1702 in Denmark. Roemer used a thermometer containing alcohol with a red dye. He created his scale by dividing the temperature between the freezing and boiling points of water into 80 degrees. Gabriel Fahrenheit, a German physicist, was the first person to use a mercury thermometer. In 1714, in Holland, he developed the Fahrenheit scale. However, he did not base his scale on the freezing and boiling points of water. Instead, for his zero point he used the lowest temperature he could create in the laboratory from a mixture of water, salt, and ice. For the other end of his scale he used the temperature of the human body for 100 degrees. Eventually the Fahrenheit scale was redesigned so that water freezes at 32 degrees, water boils at 212 degrees, and the scale between freezing and boiling is divided into 180 degrees. In 1742, Anders Celsius, a Swedish astronomer, invented a scale in which there were 100 degrees between freezing and boiling. This scale was called the centigrade scale. In 1948 this official scale of the metric system was named the Celsius scale in honor of Anders Celsius. Most countries in the world use the Celsius scale. Figure 26.2: A comparison of the Fahrenheit and Celsius temperature scales. Figure 26.3: Different types of thermometers measure different physical changes in substances. 444

5 Thermometers Thermometers Most materials expand with temperature How does a common thermometer work? You have used a thermometer all your life but might not know how it works. The most common thermometers contain either a red fluid, which is alcohol containing a small amount of red dye, or a silvery fluid, which is mercury. You may have also used a thermometer with a digital electronic readout. Thermometers can detect the physical changes in materials due to change in temperature. Different types of thermometers measure different physical changes. Most materials expand when you raise the temperature. The expansion comes from the increase in molecular motion that goes with the rise in temperature. If atoms are moving around more, they tend to bump each other apart and take up more space. The most obvious example is that gas expands when it heats up. You can see this if you heat or cool a balloon. The expansion of a liquid is not as great, but we can easily observe it. Thermal expansion is the basic principle of a thermometer. The expansion of the liquid is directly proportional to the change in temperature. For example, for every degree the thermometer heats up, the fluid inside might expand so that it takes up one more millimeter of space in the tube. Temperature changes and bridges Most solids also expand due to an increase in temperature, but the increase is very small. For solid steel the thermal expansion in on the order of one tenthousandth. This means that a 1-meter steel rod will expand 0.01 millimeters for every degree Celsius of temperature increase. Although this may be difficult to detect, temperature changes can have dramatic effects on larger structures such as buildings and bridges. For instance, a 100-meter-long bridge could be up to 10 centimeters longer on a hot summer day than on a cold winter day. In order to prevent damage to the bridge, civil engineers use expansion joints in bridges as shown in figure Figure 26.4: The expansion of the liquid in a thermometer is directly proportional to increase in temperature. Figure 26.5: In order to prevent damage due to temperature changes, civil engineers use expansion joints in bridges Temperature Scales 445

6 446 Digital thermometers How does a thermostat work? Another physical property that changes with temperature is electrical resistance. The resistance of a metal wire will increase with temperature. Since the metal is hotter, and the metal atoms are shaking more, there is more resistance to electrons passing through the wire. Digital thermometers measure this change in resistance. Most commonly, platinum metal is used in digital thermometers. You probably have a thermostat in your home. A thermostat turns on a heater (or air conditioner) based on the temperature. If the temperature in the room is too hot, the thermostat sends an electrical signal to your furnace to shut it off. Simple thermostats use a bimetallic strip to make a switch. We mentioned earlier that metals expand with an increase in temperature. Different metals expand at different rates. If you take two different metals and fix them together in a strip, the strip will bend when heated. The metal on the bottom (dark) expands more than the metal on the top (blue) and the difference is what causes the bending. In a thermostat, this bending moves a switch. Science in your home Have you ever had trouble opening a jar of salsa or mayonnaise because the lid was put on too tight? One method of opening the jar is to run the it under warm water. As the glass jar and the metal lid heat up, they will both expand. However, the rate of expansion of metal is over twice the rate of expansion of glass. Thus the lid will loosen as you heat up the jar! Liquid-crystal thermometers Some thermometers, often used on the outside of aquariums, contain liquid crystals that change color based on temperature. These liquid crystals are derived from cholesterol and were discovered in 1838 by Austrian botanist Freidrich Reinitfer. We now use these crystals by trapping them between two thin sheets of plastic, in a layer one-tenth of a millimeter thick. These are the same crystals that can be found in a mood ring. If you place a liquid crystal thermometer on your skin you will see it change color. As temperature increases, the molecules of the liquid crystal bump into each other more and more. This causes a change in the structure of the crystals, which in turn affects their color. These thermometers are able to accurately determine the temperature between 65 F and 85 F.

7 26.2 Measuring Changes in Heat You know that energy can take many forms such as kinetic energy, gravitational potential energy, electrical potential energy, and chemical potential energy. In this section, we explore thermal energy and how electrical energy becomes thermal energy. You will see how thermal energy increases the temperature of an object. You will also develop a relationship between the rate of increase in temperature of water and the increase in thermal energy of water. Temperature, thermal energy, and heat Changing temperature changes energy What is thermal energy? Heat and thermal energy Nature never creates or destroys energy; energy only gets converted from one form to another. Changes in temperature involve changes in energy. When you heat a pot of soup with an electric hot plate, electrical energy is converted into thermal energy. What, exactly, is thermal energy? Thermal energy and temperature are not the same. Temperature, as you have learned, measures the average kinetic energy of the molecules inside an object. Thermal energy is the sum of all the kinetic and potential energies of the molecules of a substance. The amount of thermal energy stored in an object depends on three things: the mass, the temperature, and the amount of energy that a particular material stores per degree. Suppose you are asked to heat up a single cup of soup or a huge pot of soup. Both have to get to the same temperature. Which takes more energy? Heating up the huge pot takes more energy because it is like heating up 100 individual cups! Because it took more energy to heat the pot of soup, it now contains more thermal energy than the cup of soup, even though they are at the same temperature. What happens when you hold an ice cream cone on a hot day? Thermal energy flows from your hand and the surrounding air to melt the ice cream. We call this flow of thermal energy heat. In the scientific sense, heat occurs only when there is a difference in temperature. Heat always flows from the warmer object to the cooler one Measuring Changes in Heat Figure 26.6: What energy changes are involved in this scenario? Figure 26.7: Where does the energy come from? Where does it go? Figure 26.8: On a hot day, the flow of thermal energy can turn your ice cream cone into a puddle if you don t eat it fast! 447

8 Measuring heat Understanding heat is important The calorie The British thermal unit The flow of thermal energy (which we call heat) is happening around us all the time. When you cook a pot of soup, thermal energy flows from the burner to the soup and to the surrounding air. You might have a fan above the stove to remove the hot air from the kitchen. A lot of the energy we consume goes toward heating or cooling our homes, businesses, and schools. Because heat is such an important concept in our lives there are three units of energy that relate directly to heat. The metric unit used to measure heat or energy is the calorie. The calorie is defined as the quantity of heat needed to increase the temperature of 1 gram of water by 1 degree Celsius. Both calories and joules are units of energy: 1 calorie = joules. Still another unit of heat you may have heard of is the British thermal unit, or Btu. The Btu is often used to describe heat produced by heating systems or heat removed by air-conditioning systems. A Btu is the quantity of heat it takes to increase the temperature of 1 pound of water by 1 degree Fahrenheit. James Prescott Joule In the 1840s, James Prescott Joule proved that the law of conservation of energy also applied to heat. Until that time, physicists only considered the law of conservation of mechanical energy, which did not include heat. Joule showed that when he converted electrical energy and kinetic energy into thermal energy, energy was still conserved. The unit for heat and energy is named in his honor. Unit Equals How do you quantify amounts of heat? 448 If you add heat to an object, how much will its temperature increase? Based on our definition of the calorie we can say that the amount of heat that flows into an object is proportional to the mass of the object times the change in temperature. This statement is known as the heat-temperature rule. Simply stated, the more heat you add to an object, the greater the increase in temperature. If you have twice as much mass of object to heat, you need twice as much energy to increase the temperature by the same amount. 1 calorie joules 1 Calorie 1000 calories 1 Btu 1055 joules 1 Btu 252 calories Figure 26.9: Conversion table for units of heat

9 Differences in materials What is specific heat? The heat equation The amount of temperature increase also depends on what you are heating. It takes more energy to raise the temperature of some materials than others. For example, suppose you put 100 calories of heat into a beaker with 100 grams of water. The temperature goes up one degree. If you apply the same amount of heat to 100 grams of iron, the temperature goes up 20 degrees! As water and iron illustrate, substances vary greatly in their ability to store thermal energy. The specific heat is a property of a substance that tells us how much the temperature goes up when a given amount of heat is added. A large specific heat means you have to put in a lot of energy for each degree increase in temperature. The whole story is told by the heat equation below. The equation tells you how much heat (Q) it takes to change the temperature ( T) of a mass (m) of a substance with specific heat (c). Figure 26.10: The temperature gains in iron and water for equal amounts of heat. Specific heats of materials Example: How much heat is needed to raise the temperature of 250 grams of water from 20 o C to 40 o C? 1. Identify the variables in the equation. Heat equation: Q = mc T Q = trying to determine m = mass of water = 250 grams c = specific heat of water = 1 calorie/g o C T = 40 o C - 20 o C = 20 o C 2. Plug the variables into the equation and solve. Q = (250 g) (1 calorie/g o C) (20 o C) Q = 5000 calories substance water 1.00 ice benzene methanol ethanol aluminum carbon silver gold specific heat calorie gram C 26.2 Measuring Changes in Heat 449

10 26.3 Specific Heat Energy is always conserved and can take many forms. Energy can be converted from kinetic energy into potential energy. Electrical energy can be converted into thermal energy. In this section, you will learn about the transfer of thermal energy from one body to another body. Flow of heat and equilibrium Energy can change from one object to another Energy loss is equal to energy gain What is thermal equilibrium? When do objects reach thermal equilibrium? When heat flows from a warm mug of hot chocolate to your hand, there is an exchange of energy for both objects. The warm mug loses energy and cools down. Your hand gains energy and warms up. When you touch the mug, your hand is in thermal contact with it. Suppose you were able to take some objects or substances in thermal contact with each other and place them in a container that would not allow any energy to leave the system. For example, you place a cup of hot coffee mixed with a cup of ice into your container. Because the mixed drink is isolated from the outside, the energy that the hot coffee loses must equal the energy that the ice gains. This is an example of the law of conservation of energy. When we are talking about heat, this law is also known as the first law of thermodynamics. Both laws state that the energy in an isolated system is conserved. Have you ever filled your kitchen sink with hot water to wash dishes? If the water was too hot, you may have added cold water to cool down the hot water. The temperature of the water in the sink eventually reaches a balance where everything is evenly warm. Whenever you have a hot object or substance in thermal contact with a cold one, heat will flow from the hot object to the cold object until they are at the same temperature, which means they are in thermal equilibrium. Objects reach thermal equilibrium when they reach the same temperature. When you submerge a thermometer in water to measure its temperature, you need to wait for a few seconds until you see the mercury or alcohol level of the thermometer stops rising. At that point, the thermometer and the water will have reached the same temperature. Both objects transfer energy (heat) until they reach thermal equilibrium. Thus, the reading you get is the thermometer s own temperature. Heat flow and the origin of the word calorie We now understand that the flow of heat is due to the transfer of energy. However, until the 1840s scientists thought that heat traveled by an invisible fluid called caloric, which comes from the Latin word for heat. We still use the word calorie even though we no longer believe in a fluid called caloric. Figure 26.11: When you hold a mug of hot chocolate, your hand is in thermal contact with the cup. 450

11 Specific heat What does specific heat mean? Water has a high specific heat Metals have low specific heats You learned in the last section that when heat flows it raises the temperature of some substances more than others. We refer to this property of a substance as its specific heat. For example, the specific heat for water is equal to It is important to point out that other substances have very different specific heat values. Water has a very high specific heat, which is why it is used as a coolant. It takes more energy to increase the temperature of water than for other substances in nature. Figure shows the specific heats for different substances. For example, aluminum has a specific heat calorie gram C 1 calorie gram C. Like most metals, aluminum has a specific heat that is five times smaller than the specific heat of water. If we add 1 calorie of energy to one gram of water, the temperature of the water will increase 1 C. However, if we add 1 calorie of energy to 1 gram of aluminum, the temperature will increase almost 5 C! Although the temperature of water did not go up by very much, the water still absorbed the heat that flowed into it. Therefore, water at a certain temperature will transfer more heat to a cooler object than most other substances. For example, 10 grams of water at 90 C will raise the temperature of a cup of cold water much higher than would 10 grams of aluminum at 90 C. substance water 1.00 ice benzene methanol ethanol aluminum carbon silver gold specific heat calorie gram C Figure 26.12: The specific heats of some common substances Specific Heat 451

12 Joseph Black Scottish chemist Joseph Black developed the theory of specific heat in Black realized the difference between heat that increases the temperature of a substance, and heat that melts or boils a substance. For instance, if we add heat to water, initially the temperature of the water increases. Black called this heat sensible heat because it could be sensed with a thermometer. Once the temperature of water reaches 100 C, it boils. Any heat added to boiling water causes water to vaporize, but does not raise the temperature. Black called the heat for melting and boiling latent heat because it could not be sensed with a thermometer. Latent means hidden. More about specific heat: the law of Dulong and Petit The specific heat of an element 452 How energy is divided More atoms per gram means higher specific heat Every substance has a different specific heat, but what physical principle gives rise to these differences? The answer was discovered in 1819 by the French physicists Pierre Louis Dulong and Alexis Therese Petit. They showed that the specific heat of an element depends on how many atoms there are per gram. One gram of a heavy element, like silver, will have fewer atoms than 1 gram of aluminum. Suppose you add one calorie of heat to two samples (aluminum and silver) of equal mass. The temperature of the silver goes up by 18 C while the aluminum only goes up by 5 C (figure 26.13). The silver sample has fewer atoms than the aluminum sample because silver atoms are heavier. When you add heat, each atom gets an equal share of the energy. If there are more atoms, each atom gets less energy. Because the energy added to the two samples is the same, each silver atom gets more energy that each aluminum atom. The temperature depends on the amount of energy per atom. If each atom gets more energy, the temperature change will be greater. This explains why the specific heat of aluminum is greater than the specific heat of silver. Aluminum has more atoms per gram, therefore it takes more energy per gram to raise the temperature. Figure 26.13: The specific heat of aluminum is greater than that of silver because aluminum has more atoms per gram than silver.

13 Review Chapter 26 Review Vocabulary review Match the following terms with the correct definition. There is one extra definition in the list that will not match any of the terms. Set One 1. Fahrenheit scale a. Temperature scale where the freezing point of water is 0 and the boiling point is Celsius scale b. A quantity used to describe the sensations of hot and cold 3. thermometer c. A device that converts temperature differences into electrical energy for running machines 4. electrical resistance d. Temperature scale where the freezing point of water is 32 and the boiling point is 212 Set Two 1. thermal energy a. The temperature rises proportionally to the mass and amount of heat added 2. heat b. The sum of the kinetic and potential energies of the molecules of a substance 3. heat-temperature rule c. Quantity of heat needed to raise the temperature of 1 gram of water by 1 Celsius 4. joule d. Energy transferred because of a temperature difference 5. temperature e. Instrument that measures temperature changes 5. calorie e. Unit of energy smaller than the calorie Set Three 1. law of conservation of energy f. A physical property that changes with temperature change a. The amount of energy it takes, per unit mass, to raise the temperature of a material one degree 2. thermal equilibrium b. Energy per unit mass that flows at the melting or boiling points of a substance 3. specific heat c. Heat flows from a hot object to a cold object until they have the same temperature 4. specific heat of water d. Energy lost by one part of a system must equal the energy gained by another part of the system 5. latent heat e. Instrument that measures temperature changes f calorie gram C f. Quantity of heat needed to raise the temperature of 1 pound of water by 1 Fahrenheit 453

14 Review Concept review 1. How would you define temperature? 2. What happens to the volume of the gas in a balloon when it is heated? 3. What happens to the length of a bar of iron when it is heated? 4. How would you define heat? 5. How would you define thermal energy? 6. Why is water used as a coolant? 7. On the Celsius scale, water boils at what temperature? a. 0 b. 32 c. 100 d Normal human body temperature on the Fahrenheit scale is closest to: a. 37 F b. 68 F c. 150 F d. 100 F 9. Water at 40 C is mixed with an equal amount of water at 40 F. The final temperature of the mixture: a. remains constant at 40 C. b. remains constant at 40 F. c. gets warmer than 40 C. d. gets warmer than 40 F. 10. Describe what happens to the individual molecules in an object when you increase its temperature, and why this causes the object s size to increase. 11. What is thermal equilibrium? 12. What does the law of conservation of energy tell us about heat transfer? 13. How does a thermometer work? 14. One liter of water at 10 C is added to 1 liter of water at 80 C. What is the final temperature of the mixture? a. 10 C b. 45 C c. 5 C d. 90 C 15. When you hold a cold can of soda in your hand, thermal energy flows: a. from the can of soda to your hand. b. from your hand to the can of soda. c. in both directions. d. There is no flow of thermal energy. 16. Due to its large mass, an iceberg has more thermal energy than a hot cup of coffee. If the cup of coffee is placed in thermal contact with an iceberg, where is energy exchanged? a. Thermal energy flows from the iceberg to the cup of coffee. b. Thermal energy flows from the cup of coffee to the iceberg. c. Thermal energy flows in both directions. d. There is no exchange of thermal energy. 454

15 Review Problems 1. Convert the Celsius temperature at which water freezes, 0 C, to degrees Fahrenheit. 2. Convert the Fahrenheit temperature at which paper burns, 451 F, to degrees Celsius. 3. Convert the Celsius temperature of the surface of the sun, which is 5,500 C, to degrees Fahrenheit. 4. Convert today s highest temperature from Fahrenheit to Celsius. 5. A teapot contains 500 milliliters of water. Five thousand calories of heat are added to the teapot. What is the increase in the temperature of the water? 6. How much energy will it take to increase the temperature of 200 milliliters of water by 12 C? 7. The power of a coffee pot is rated at 900 watts. It can heat 1 liter of water in 2 minutes. a. How much electrical energy does the coffee pot use in this process? b. Assuming the coffee pot has an efficiency of 30 percent, how much of the electrical energy becomes thermal energy in the water? c. What is the increase in the temperature of the water? 8. One liter of water at 10 C is added to 4 liters of water at 80 C. What is the equilibrium temperature of the mixture? 9. One liter of water at 20 C is mixed with 3 liters of water at 80 C. What is the equilibrium temperature of the mixture? 10. In the problem above, how many calories of heat are transferred from the hot water to the cold water? 11. Two liters of water at 40 C are added to 2 liters of water at 80 C. The final temperature of the mixture is 60 C. How many calories of heat flow from the hot water to the cold water? (Hint: The mass of 1 liter of water is 1000 grams.) 12. Two beakers each contain 1 kilogram of water at 0 C. One kilogram of gold at 100 C is dropped into one beaker. One kilogram of aluminum at 100 C is dropped into the other beaker. a. Compare the amount of thermal energy contained in the aluminum and gold. b. After each beaker has reached thermal equilibrium, describe whether the temperatures are the same, or different. If they are different, describe which is warmer and which is colder. c. Explain why you gave you answer to part (b). Use the concept of specific heat in your explanation. 455

16 Review Applying your knowledge 1. Look at or have someone show you the water level in an automobile radiator. You will notice that the radiator is filled up to the cap with water. Next to the radiator there is an overflow container. As the car runs and the water get very hot, what happens to the water? What have engineers included in the design of an automobile radiator system to return the water from the overflow into the radiator? 2. The first settlers in Colorado were very concerned about fruits and vegetables freezing in their root cellars overnight. They soon realized that if they placed a large tub of water in the cellar, the food would not freeze. Explain why the food would not freeze. 3. If you keep lowering the temperature of a material, the atoms vibrate less and less. If you could eventually reach a low enough temperature, the atoms might not vibrate at all. Is this possible, and what does it mean for the temperature scale? Is it possible to keep lowering the temperature indefinitely? 4. For one or more of the following, write a short paper or give a presentation on your research: a. In the 1860s, the English physicist James Clerk Maxwell ( ) and the Austrian physicist Ludwig Boltzmann ( ) first gave a rigorous analysis of temperature in terms of the average kinetic energy of the molecules of a substance. Explore their lives and their contributions to the development of the theory of temperature. b. Lord Kelvin ( ), a British physicist, developed the idea of absolute zero, the coldest temperature attainable. The Kelvin temperature scale is named in his honor. Research absolute zero, the Kelvin scale, and the life of Lord Kelvin. c. Scottish chemist Joseph Black developed the theories of specific and latent heat. Research his life and how he made these discoveries. 456