Energy Joules The units for energy are Joules=kg m 2 /s 2 It has the units of mass velocity velocity One example of a type of energy is kinetic energy, the energy of motion, which happens to be (1/2)mv 2 for an object of mass m moving at speed v For an OSU running back: m=100 kg v=10 m/s (i.e. can sprint 100m in 10 seconds) kinetic energy = (1/2)(100kg)(10m/s) 2 =5000 Joules Forms of Energy Kinetic energy = energy from motion Gravitational potential energy = energy from sitting in a gravitational field Thermal energy = energy associated with the temperature of an object Chemical energy = energy stored in the chemical bonds of something Energy of a photon Chemical Energy Calories (of food) are a measure of chemical energy 1 food calorie 4000 Joules The energy is stored in the chemical bonds of the proteins, sugars etc. the kinetic energy of the running back is equal to about ¼ of an M&M (about 4-5 calories per M&M) 1 gram of TNT is officially 4182 Joules The biggest difference between M&Ms and TNT is how fast you can extract the energy Gravitational Energy There is gravitational potential energy associated with where you sit in a gravitational field The units for energy are Joules=kg m 2 /s 2 Conservation of Energy You can change the type of energy, but the total amount of energy in all the forms is conserved. It has the units of mass height gravitational acceleration 5000 Joules = (100 kg) (5 m) (10 m/s 2 ) So the linebacker s kinetic energy is about the same as he would have from falling 5m 1
An Illustration Put a book on top of a ladder it has gravitational potential energy Let it drop off the ladder the gravitational potential energy is converted into kinetic energy (motion) Light the Messenger When it hits the ground, the kinetic energy is converted (in the end) into heat (thermal energy) Key Ideas about Light Light is Electromagnetic Radiation Light has a finite velocity the speed of light Light can be thought of as Waves, or Particles (Photons) Electromagnetic Spectrum Sequence of photon energies Inverse Square Law of Brightness Electromagnetic Radiation Light is Electromagnetic Radiation. Self-propagating Electromagnetic disturbance that moves at the speed of light: c = 300,000 km/sec Can treat light as either: Electromagnetic Waves Photons (particles of light) The Speed of Light The speed of light (in vacuum) is constant: c = 3.0 10 8 m/s = 300,000 km/s While this is fast, the solar system is big, so light travel times have measurable effects. Light Across the Solar System Sun E 1AU 4.2AU Jupiter at opposition is 4.2 AU from Earth the light travel time is 2100 seconds Jup Jup 6.2 AU Sun E Jupiter at conjunction is 6.2 AU from Earth the light travel time is 3100 seconds What happens to a clock at Jupiter observed from Earth? 2
A Clock at Jupiter The moons of Jupiter supply a clock at Jupiter When we observe where the moons are, we are really observing them at a time t=(distance to Jupiter)/(speed of light) earlier. As we just worked out, this varies by 1000 seconds between opposition and conjunction. Suppose we work out when Io should be eclipsed by studying Io s orbit when Jupiter is at opposition, and then measure when Io is eclipsed when Jupiter is at conjunction we would see the eclipse 1000 seconds late because of the extra propagation time At conjunction At opposition This was realized in 1676 (Romer) Earth Sun Sun Earth t=(2au)/c=1000sec Jupiter and Io Jupiter and Io Romer got t right from the timing of eclipses of the Galilean moons by Jupiter, understood it was due to the speed of light, but couldn t determine c accurately because he didn t have an accurate measurement of the AU. Making Waves A Wave is any periodic fluctuation traveling through a medium that carries energy. periodic - regularly repeating pattern Examples: Water Waves: periodic fluctuations in the height of the water traveling across the surface. Sound Waves: periodic fluctuation in the air pressure (compression waves) traveling through the air. Measuring Waves Waves are described by two numbers: Wavelength ( ): Distance between wave crests. Frequency (f): Number of wave crests passing per second. The wave speed, c, is the product of these: c = f Wavelength ( ) Speed (c) Frequency (f) (# waves/second) 3
Examples of Waves Ocean waves: = 100 m, f = 0.1/second; wave speed: c = 10 m/second (36 km/hr) Speed depends on water depth, salinity, etc. Sound waves (A 440): = 0.73 m, f = 440/second; wave speed: c = 320 m/second (1150 km/hr) For sound, frequency = pitch. Light as electromagnetic waves Can treat light as an Electromagnetic Wave Fluctuation in the intensity of electric and magnetic fields. Travels through a vacuum at the speed of light. Doesn t need a medium to wave in. Speed of light is a constant for all light waves: c = 300,000 km/sec Independent of wavelength or frequency. Electromagnetic Wave Visible Light Waves Wavelengths: 400 700 nanometers (nm) 1 nm = 10-9 meters Frequencies: 7.5 10 14 4.3 10 14 waves/second Visible Spectrum: Red Orange Yellow Green Blue Indigo Violet 700 nm ------------- 550 nm ------------ 400 nm R O Y G. B I V Photons: Particles of Light Can also treat light as particles or Photons. Photon: Massless particle that carries energy at the speed of light. Photon Energy: E = hf f = frequency of the light h = Planck s Constant 4
Photoelectric Effect Demonstration of the particle nature of light: Light hitting a piece of metal (for example, cesium) kicks out electrons. Low-frequency light (e.g., red): No electrons kicked out, no matter how bright. High-frequency light (e.g., blue): Number of electrons kicked out is proportional to the brightness of the light. Electron energies are proportional to the frequency. Photoelectric Effect Cesium Photons hitting the metal will knock out single electrons, but only if they have enough energy to break the electrons free of the metal. Demonstrating this won Einstein the Nobel Prize. The Electromagnetic Spectrum Sequence of photon energies from low to high is called the Electromagnetic Spectrum low energy = low frequency = long wavelength Examples: Radio Waves, Microwaves, Infrared high energy = high frequency = short wavelength Examples: Ultraviolet, X-rays, Gamma Rays Parts of the Spectrum Type of Radiation Wavelength Range Gamma Rays < 0.01 nm X-Rays 0.01 10 nm Ultraviolet 10 400 nm Visible Light 400 700 nm Infrared 700 10 5 nm (0.1 mm) Microwaves 0.1mm 10mm Radio > 1 cm The Electromagnetic Spectrum What is a Spectrum? A spectrum is the distribution of the light emitted from a source in energy (or wavelength or frequency) How many photons of each energy are emitted by the light source? Spectra are observed by passing light through a spectrograph: Breaks the light into its component wavelengths and spreads them apart (dispersion). Uses either prisms or diffraction gratings. 5
Prisms disperse light into its component colors Increasing Energy White Light Prism Spectrum Modern Spectrograph How Bright is a Light Source? We need to quantify how bright an object is. Wave picture of light: Brightness corresponds to the amplitude of the wave (height of the wave crests). Particle (photon) picture of light: Brightness corresponds to the number of photons per second from the light source. The photon picture is the more useful. Luminosity Luminosity is the total energy emitted by an object. Measured in Power Units: (Energy emitted)/second (e.g., Watts) Independent of Distance Important for measuring the total energy output of a object (e.g. the Sun). Luminosity and Energy luminosity is the amount of energy you get per unit time 1 Watt = 1 Joule/second In this case we are interested in the luminosity from the sun 6
The Solar Luminosity The luminosity of the Sun is L =3.9 10 26 Watts=joules/second The energy comes from nuclear fusion (converting Hydrogen into Helium) in the Sun s core, and the Sun has enough fuel to run for about 10 billion years. We re about halfway through the solar lifetime. A big electric power plant on earth produces 10 9 Watts, so the Sun is the equivalent of 400,000,000,000,000,000 (4 10 17 ) of them. Apparent Brightness or Flux Measures how bright an object appears to be to a distant observer. What we can actually measure directly ( observable ) Measured in Flux Units: Energy/second/area=Watts/m 2 from the source. Depends on the Distance to the object. The total mass of the Earth s oceans is about 10 21 kg and it takes 2.7 10 6 joules (140 M&Ms) to evaporate 1kg of water starting from freezing. Thus, you need 3 10 27 joules to vaporize Earth s oceans, or about 10 seconds worth of the Sun s energy output. Inverse Square Law of Brightness d=1 B=1 d=2 B=1/4 d=3 B=1/9 The Apparent Brightness of a source is inversely proportional to the square of its distance: B 1 d 2 2-times Closer = 4-times Brighter 2-times Farther = 4-times Fainter The Solar Flux The flux from the Sun at distance d is simply the of the Sun spread over the surface of a sphere of radius d : Luminosity Brightness or Flux Area AU 1400 Watts/m d 2 Luminosity 2 4 d 2 luminosity Planets further from the Sun should be colder since the receive less solar heating Solar Power At Earth The energy a planet receives (per second) is the incident flux (energy per unit area per second) times the projected area of the planet So the Earth receives 2 10 17 Watts of solar radiation= 177 million 1 Gigawatt power plants Total human energy use is about 10 Terawatts (10 13 Watts), or about 0.005% of the incident solar radiation. In theory, with perfect solar power cells, a 100x100km array could supply all our current energy use. In practice life is more difficult the flux at the surface is smaller, the sun is up only ½ the day, and even the best solar cells are only about 25% efficient, so you only generate about 100 Watts/m 2 of electricity and need 300x300km. 7
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