Ch12. Temperature and HeatCommon Temperature Scales A number of different temperature scales have been devised, two popular choices being the Celsius (formerly, centigrade) and Fahrenheit scales.
On the Celsius scale, an ice point of 0 °C (0 degrees Celsius) and a steam point of 100 °C were selected. On the Fahrenheit scale, an ice point of 32 °F (32 degrees Fahrenheit) and a steam point of 212 °F were chosen. The Celsius scale is used worldwide, while the Fahrenheit scale is used mostly in the United States. The temperature of the human body is about 37 °C, where the symbol °C stands for “degrees Celsius.” However, the change between two temperatures is specified in “Celsius degrees ”(C°)—not in “degrees Celsius”. The separation between the ice and steam points on the Celsius scale is divided into 100 Celsius degrees, while on the Fahrenheit scale the separation is divided into 180 Fahrenheit degrees. Therefore, the size of the Celsius degree is larger than that of the Fahrenheit degree by a factor of , or .
Reasoning and Solution A temperature of 98.6 °F is 66.6 Fahrenheit degrees above the ice point of 32.0 °F. Since , the difference of 66.6 F° is equivalent to Thus, the person’s temperature is 37.0 Celsius degrees above the ice point. Adding 37.0 Celsius degrees to the ice point of 0 °C on the Celsius scale gives a Celsius temperature of Example 1. Converting from a Fahrenheit to a Celsius Temperature A healthy person has an oral temperature of 98.6 °F. What would this reading be on the Celsius scale?
The temperature, then, is 36.0 Fahrenheit degrees below the ice point. Subtracting 36.0 Fahrenheit degrees from the ice point of 32.0 °F on the Fahrenheit scale gives a Fahrenheit temperature of Example 2. Converting from a Celsius to a Fahrenheit Temperature A time and temperature sign on a bank indicates that the outdoor temperature is –20.0 °C. Find the corresponding temperature on the Fahrenheit scale .
Reasoning Strategy Converting Between Different Temperature Scales 1. Determine the magnitude of the difference between the stated temperature and the ice point on the initial scale. 2. Convert this number of degrees from one scale to the other scale by using the fact that. 3.Add or subtract the number of degrees on the new scale to or from the ice point on the new scale.
Check Your Understanding 1 On a new temperature scale the steam point is 348 °X, and the ice point is 112 °X. What is the temperature on this scale that corresponds to 28.0 °C? 178 °X
The Kelvin Temperature Scale Kelvin temperature scale was introduced by the Scottish physicist William Thompson (Lord Kelvin, 1824–1907), and in his honor each degree on the scale is called a kelvin (K). By international agreement, the symbol K is not written with a degree sign (°), nor is the word “degrees” used when quoting temperatures. For example, a temperature of 300 K (not 300 °K) is read as “three hundred kelvins,” not “three hundred degrees kelvin.” The kelvin is the SI base unit for temperature.
The ice point (0 °C) occurs at 273.15 K on the Kelvin scale. When a gas confined to a fixed volume is heated, its pressure increases. Conversely, when the gas is cooled, its pressure decreases. The change in gas pressure with temperature is the basis for the constant-volume gas thermometer.
A plot of absolute pressure versus temperature for a low-density gas at constant volume. The graph is a straight line and, when extrapolated (dashed line), crosses the temperature axis at –273.15 °C. “Absolute zero” means that temperatures lower than –273.15 °C cannot be reached by continually cooling a gas or any other substance.
Thermometers A property that changes with temperature is called a thermometric property. The thermocouple is a thermometer used extensively in scientific laboratories. It consists of thin wires of different metals, welded together at the ends to form two junctions.
One of the junctions, called the “hot” junction, is placed in thermal contact with the object whose temperature is being measured. The other junction, termed the “reference” junction, is kept at a known constant temperature (usually an ice–water mixture at 0 °C). The thermocouple generates a voltage that depends on the difference in temperature between the two junctions. This voltage is the thermometric property and is measured by a voltmeter.
Because this electrical resistance changes with temperature, electrical resistance is another thermometric property. Electrical resistance thermometers are often made from platinum wire, because platinum has excellent mechanical and electrical properties in the temperature range from –270 °C to +700 °C. The electrical resistance of platinum wire is known as a function of temperature. Thus, the temperature of a substance can be determined by placing the resistance thermometer in thermal contact with the substance and measuring the resistance of the platinum wire.
Radiation emitted by an object can also be used to indicate temperature. At low to moderate temperatures, the predominant radiation emitted is infrared. As the temperature is raised, the intensity of the radiation increases substantially. “Thermal painting” is called a thermograph or thermogram. Thermography is an important diagnostic tool in medicine.
Linear Thermal Expansion NORMAL SOLIDS The increase in any one dimension of a solid is called linear expansion . When the temperature of a rod is raised by T, the length of the rod increases by L .
For modest temperature changes, experiments show that the change in length is directly proportional to the change in temperature In addition, the change in length is proportional to the initial length of the rod. L is proportional to both L0 and T ( ) by using a proportionality constant , which is called the coefficient of linear expansion.
LINEAR THERMAL EXPANSION OF A SOLID The length L0 of an object changes by an amount L when its temperature changes by an amount T: where is the coefficient of linear expansion. Common Unit for the Coefficient of Linear Expansion:
A concrete sidewalk is constructed between two buildings on a day when the temperature is 25 °C. The sidewalk consists of two slabs, each three meters in length and of negligible thickness . As the temperature rises to 38 °C, the slabs expand, but no space is provided for thermal expansion. The buildings do not move, so the slabs buckle upward. Determine the vertical distance y in part b of the drawing.
Antiscalding device screws onto the end of a faucet and quickly shuts off the flow of water when it becomes too hot. As the water temperature rises, the actuator spring expands and pushes the plunger forward, shutting off the flow. When the water cools, the spring contracts and the water flow resumes.
THERMAL STRESS: Example 4. The Stress on a Steel Beam A steel beam is used in the roadbed of a bridge. The beam is mounted between two concrete supports when the temperature is 23 °C, with no room provided for thermal expansion. What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the beam from expanding when the temperature rises to 42 °C?
Y = 2.0 × 1011 N/m2 = 12 × 10–6 (C°) –1 DT = 19 C°
THE BIMETALLIC STRIP A bimetallic strip is made from two thin strips of metal that have different coefficients of linear expansion. Bass Steel
Bimetallic strips are frequently used as adjustable automatic switches in electrical appliances.
THE EXPANSION OF HOLES: Conceptual Example 5. Do Holes Expand or Contract When the Temperature Increases? Eight square tiles that are arranged to form a square pattern with a hole in the center. If the tiles are heated, what happens to the size of the hole?
The hole expands just as if it were made of the material of the surrounding tiles.
Example 6. A Heated Engagement Ring A gold engagement ring has an inner diameter of 1.5 × 10–2 m and a temperature of 27 °C. The ring falls into a sink of hot water whose temperature is 49 °C. What is the change in the diameter of the hole in the ring? a = 14 × 10–6 (C°)–1
Conceptual Example 7. Expanding Cylinders In a cross-sectional view of three cylinders, A, B, and C, each is made from a different material: one is lead, one is brass, and one is steel. All three have the same temperature, and they barely fit inside each other. As the cylinders are heated to the same, but higher, temperature, cylinder C falls off, while cylinder A becomes tightly wedged to cylinder B. Which cylinder is made from which material?
A = brass, B = steel, and C = lead A = lead, B = steel, and C = brass
Check Your Understanding 2 • A metal ball has a diameter that is slightly greater than the diameter of a hole that has been cut into a metal plate. The coefficient of linear thermal expansion for the metal from which the ball is made is greater than that for the metal of the plate. Which one or more of the following procedures can be used to make the ball pass through the hole? • Raise the temperatures of the ball and the plate by the same amount. • Lower the temperatures of the ball and the plate by the same amount. • Heat the ball and cool the plate. • Cool the ball and heat the plate. b & d
Volume Thermal Expansion VOLUME THERMAL EXPANSION The volume V0 of an object changes by an amount V when its temperature changes by an amount T: where is the coefficient of volume expansion. Common Unit for the Coefficient of Volume Expansion: (C°) –1 b = 3a.
Example 8. An Automobile Radiator A small plastic container, called the coolant reservoir, catches the radiator fluid that overflows when an automobile engine becomes hot . The radiator is made of copper, and the coolant has a coefficient of volume expansion of . If the radiator is filled to its 15-quart capacity when the engine is cold (6.0 °C), how much overflow from the radiator will spill into the reservoir when the coolant reaches its operating temperature of 92 °C?
The fact that water has its greatest density at 4 °C, rather than at 0 °C, has important consequences for the way in which a lake freezes.
The fact that the density of ice is smaller than the density of water has an important consequence for home owners, who have to contend with the possibility of bursting water pipes during severe winters.
Heat and Internal Energy • Heat is energy in transit from hot to cold. • Heat flows from the hotter coffee cup to the colder hand. • Heat flows from the warmer hand to the colder glass of ice water.
DEFINITION OF HEAT Heat is energy that flows from a higher-temperature object to a lower-temperature object because of the difference in temperatures. SI Unit of Heat: joule (J) The internal energy of a substance is the sum of the molecular kinetic energy (due to the random motion of the molecules), the molecular potential energy (due to forces that act between the atoms of a molecule and between molecules), and other kinds of molecular energy. When heat flows in circumstances where the work done is negligible, the internal energy of the hot substance decreases and the internal energy of the cold substance increases.
Heat and Temperature Change: Specific Heat Capacity SOLIDS AND LIQUIDS HEAT SUPPLIED OR REMOVED IN CHANGING THE TEMPERATURE OF A SUBSTANCE The heat Q that must be supplied or removed to change the temperature of a substance of mass m by an amount T is where c is the specific heat capacity of the substance. Common Unit for Specific Heat Capacity: J/(kg·C°)
Example 9. A Hot Jogger 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?
(a ) Example 10. Taking a Hot Shower Cold water at a temperature of 15 °C enters a heater, and the resulting hot water has a temperature of 61 °C. A person uses 120 kg of hot water in taking a shower. (a) Find the energy needed to heat the water. (b) Assuming that the utility company charges $0.10 per kilowatt·hour for electrical energy, determine the cost of heating the water.
(b) At a cost of $0.10 per kWh, the bill for the heat is $0.64 or 64 cents.
GASES The value of the specific heat capacity depends on whether the pressure or volume is held constant while energy in the form of heat is added to or removed from a substance. The distinction between constant pressure and constant volume is usually not important for solids and liquids but is significant for gases.
HEAT UNITS OTHER THAN THE JOULE There are three heat units other than the joule in common use. One kilocalorie (1 kcal) was defined historically as the amount of heat needed to raise the temperature of one kilogram of water by one Celsius degree. one calorie (1 cal) was defined as the amount of heat needed to raise the temperature of one gram of water by one Celsius degree The British thermal unit (Btu) is the other commonly used heat unit and was defined historically as the amount of heat needed to raise the temperature of one pound of water by one Fahrenheit degree.