Thermal Expansion • When a solid is heated, its atoms spread out in all dimensions. • Consequences of thermal expansion may be desirable or undesirable!
Thermal Expansion • To calculate a change in length due to thermal expansion: Δl = αliΔt
Thermal Expansion • α is the coefficient of thermal expansion • different for each material • units: °C-1 or K-1 Δl = αliΔt
Thermal Expansion • Δl and li must be in the same units of length • Δt and α must use the same temperature units Δl = αliΔt
Thermal Expansion • bimetallic strips take advantage of different rates of expansion of different materials • thermostats
Thermal Expansion • Expansion of volume can be similarly calculated: • β is the coefficient of volume expansion. • β = 3α ΔV = β ViΔt
Thermal Expansion • Liquids respond to temperature changes much more than solids do. • The same equation can be used for liquid expansion. ΔV = β ViΔt
Thermal Expansion • Example 14-3: • How much does the gasoline expand? • How much does the tank expand? • How much gas spills?
Thermal Expansion • Gases also expand in volume with changes in temperature; this is discussed in more detail later in the chapter.
Thermometers • Galileo—thermoscope • drawback: also responded to changes in air pressure
Thermometers • Gas thermometers are more accurate but less convenient. • Now liquid thermometers use liquids sealed in glass tubes under vacuum.
Liquid Thermometers • must be calibrated • must be sensitive enough that a small change in temperature produces a noticeable change in liquid level
Liquid Thermometers • should respond quickly to changes in temperature • mass must be small in relation to the bulk of the object whose temperature is being measured
Liquid Thermometers • medium used in thermometer must be appropriate for the range of temperatures being measured
Thermometric • A thermometric property of a substance is any measurable property that changes in proportion to a corresponding change in temperature.
Thermometric • other temperature-measuring instruments: • resistive temperature detectors (RTD) • thermocouple junctions
Thermometric • other temperature-measuring instruments: • mechanical thermometers • digital thermometers
Temperature Scales • Fahrenheit • After trying other things, the reference points became 32° (freezing point of water) and 212° (boiling point of water).
Temperature Scales • Celsius • This scale sets the freezing point of water at 0° and the boiling point of water at 100°.
Temperature Scales • Absolute or Kelvin • emphasized an “absolute zero” • absolute zero is 0K or about -273.15°C
Temperature Scales • Absolute or Kelvin • also uses triple point of water as a reference • the degree symbol (°) is not used
Conversions • Celsius (tC) and Kelvin (T): • T = tC + 273.15 • tC = T – 273.15
Conversions • Fahrenheit (tF) to Celsius (tC): • tC = 5/9(tF + 40°) – 40° • tC = 5/9(tF – 32°)
Conversions • Celsius (tC) to Fahrenheit (tF): • tF = 9/5(tC + 40°) – 40° • tF = 9/5(tC) + 32°
Conversions • To convert between Kelvin and Fahrenheit, first convert to Celsius and then to the desired unit.
Ideal Gas • Ideal gas particles have no volume. • Ideal gas particles do not interact except when they have perfectly elastic collisions.
Charles’s Law • deals with the effect of temperature on the volume of a gas at a constant pressure • related to the computation of absolute zero temperature
V1 V2 = T1 T2 Charles’s Law • temperature must be expressed in Kelvin for this and all other gas laws
Charles’s Law • When doing problems involving these laws, consider in advance: Will the final quantity be larger or smaller than the original?
Boyle’s Law • deals with the effect of pressure on the volume of a gas at a constant temperature • invented what we call a “Boyle’s law tube” to investigate this
Boyle’s Law • volume is inversely proportional to pressure, if the temperature is constant V1P1 = V2P2
P1 P2 = T1 T2 Gay-Lussac’s Law • deals with the effects of pressure and temperature of a gas at a constant volume
P1V1 P2V2 = T1 T2 Combined Gas Law • does not require that any single quantity remain constant
Ideal Gas Law • PV = KT • K is a temperature-dependent constant • K = kN • N = number of particles • k = 1.381 × 10-23 J/K
Ideal Gas Law • k = 1.381 × 10-23 J/K is called Boltzmann’s constant • k · NA provides the universal gas constant (R): R 8.315 J/(K·mol)
Ideal Gas Law • The ideal gas law is usually written as: PV = nRT • The units used for R must be consistent with those given in the data!
Ideal Gas Law • standard temperature and pressure (STP): 273.15 K 1.013 × 105 Pa
Real Gases • The ideal gas model is not as accurate at higher pressures and lower temperatures.
Real Gases • Other more accurate and more complicated equations have been developed. • Johannes van der Waals