Lecture 6

Matter and Energy in the Universe

Except for a few bodies in the Solar System (Moon, Mars, meteorites) the only way to learn about the Universe is from the light we receive from the celestial objects (it would take us 10⁵ years to get to the nearest star!).

To understand the nature of the Universe we are forced to read the message encoded in the light we receive, for which astronomers use the technique called spectroscopy. Basically, it consists in using a prism to split the light in its component colors.

Newton (1660's) was the first to describe that the light from the Sun is made of a mixture of light of violet, blue, green, yellow, orange, red colors called the visible spectrum. The Sun emits most of the light in the yellow range. Hotter stars emit more light in the blue, while cooler stars emit more red light.




In 1810's Fraunhofer (German physicist) magnified the Sun's spectrum using a grating and discovered dark lines



These lines are caused by atoms in the solar atmosphere that absorb light at specific places in the spectrum. Since each element produces a unique absorption pattern, the identification of such lines allows us to tell the chemical composition of a star! To date, we know that the most distant stars are made of the same elements present on Earth.

I. Basics of matter

• Matter is made of atoms (indivisible unit of matter)
  • The idea that matter is composed of atoms goes back to Greek philosopher Democritus (over 2000 years ago)

  • The structure of the atom began to be revealed with the experiments by Joseph J. Thomson in 1897 that led to the discovery of a fundamental building block of matter, the electron which has a negative charge and is 2000x lighter than the lightest atom. Click here
  for a history of the discovery.

  J.J. Thompson

  • Ernest Rutherford's experiment in 1908 revealed the structure of the atom

    E. Rutherford

    Summary of the main results of the experiment:

    • 1. most alpha particles (Helium atoms minus electrons) pass right through gold fold

    • 2. a small fraction of alphas are deflected very slightly

    • 3. a small fraction of alphas are deflected almost straight back

    Applet for the interpretation:

    • 1. The atom is mostly empty space

    • 2. The nucleus is positively charged as is the alpha particle

    • 3. The nucleus carries most of the atom's mass

  • Atomic model: A nucleus with a positive charge surrounded by a cloud of negatively charged electrons

    

    The nucleus consists of positively charged particles called protons and neutral particles called neutrons, each with a mass of 1.7 x 10^-27 kg. The number of protrons equals the number of electrons so an atom is electrically neutral. Q: If charges of the same sign repel each other, why does the nucleus remain bound?

• There are over 100 different types of atoms that differ in their number of protons (H, He, Li,...)

• The number of protons is called the atomic number, which defines also the number of electrons (why?)

• Atoms can combine with other atoms to form molecules. They do so by giving up or receiving electrons in a process called chemical reaction, so the chemical properties of the element are given by the number of electrons.

• Chemical reactions dictate the way that atoms and molecules combine to form different compounds, but one atom cannot be changed into another by chemical reactions.

• Atoms with the same atomic number may have different neutrons. They do not change the chemical properties of the element but only its mass. Atoms with the same atomic number but different mass are called isotopes.

• The periodic table is a sequence of atoms with increasing number of protons. It has been organized according to the chemical properties of the elements.
  • At the far right are the noble gases that do not react with other atoms

  • Elements at the far left are highly reactive, but they only do it with elements in the VII column (NaCl)

    

II. Energy

Energy is something that causes a change to a system, at the macroscopic or microscopic level. There are different forms of energy.

• Kinetic energy: any given body has kinetic energy if it is in motion.
  • KE = 1/2 m v²

  • Fast moving object has more: double speed, get 4x energy

  • Massive object has more: double mass, get 2x energy

  • Units: [kg m² /s²] = joules (1 calorie = 4.186 J)

  • Click here
  for an example

• Potential energy: Stored energy waiting to be released

  • A tensioned spring: even at rest it has the potential for creating motion

  • Chemical energy: wood, gasoline, dinamite are fuels that can release energy when electrons in atoms and molecules change their configuration

  • Electrical Energy: fresh battery

  • Electromagnetic radiation: light (ex: Sun)

  • Nuclear energy can be released if the configuration of subatomic particles in the nucleus of an atom change

  • Gravitational energy:
    • brick moved up to table will release energy when falling (GE --> KE)

    • hydroelectric plant

    • GE = m g h (see example
    )

III. Heat and Temperature

• Heat is a form of energy that can flow from one place to another
  • Rub your hands. Friction converts KE into heat

  • Joule (1840) weight turns paddles as it drops, temperature of water rises. He showed that KE can be converted into heat. What happens is that the motion of the paddles caused water molecules to move faster through friction. Hence, heat is a microscopic form of KE.

    Joule's experiment

  • Temperature:
    • measures motion of molecules and atoms (kinetic energy) --> Higher T = faster microscopic motions

    • Does not measure total amount of heat in object

      (example: drop of boiling water vs. cup of boiling water have same T, yet different thermal energy)

  • Heat is the amount of thermal energy contained in the microscopic motions

  • Temperature scales
    • Celsius:
      0^o = freezing point of water

      100^o = boiling point of water

    • Kelvin:
      0^o = absolute zero

      273^o = freezing point of water

      373^o = boiling point of water

      295^o = room temperature

    At high temperatures, say millions of degrees, scales are effectively the same

  • Velocities of atoms and molecules in a gas
    • 1/2 m v² = 3/2 k T (Maxwell and Boltzmann)

    • k = 1.38 x 10^-23 J/^oK (Boltzmann's constant)

    • T = m v² / 3 k

    • v = (3 k T / m)^1/2 (low mass atoms move faster)

    • Click here
    for an example

  IV. Transformation and conservation of energy

• The law of the conservation of energy means that energy can neither be created or destroyed, only transformed from one form to another.

• Examples of energy transformation
  • Joule's experiment: Gravitational energy --> Kinetic Energy --> Heat

  • Potential energy may be converted into kinetic energy of motion:

    

    

  • Potential energy may be converted into kinetic energy of motion, and in turn to other forms such as electrical energy. Thus, water behind a dam flows to lower levels through turbines that turn electric generators, producing electric energy plus some unusable heat energy resulting from turbulence and friction. Which is the ultimate energy source of a hydroelectric plant?

  • Kepler's second law
    • In an elliptical orbit about the Sun, the speed of a planet is related to its distance from the Sun

    • Planet has more gravitational potential energy and least kinetic energy when furthest from Sun

    • Planet has least potential energy and most kinetic energy when closest to the Sun

  • Asteroid impact
    • Asteroid hurtles through space at 10 km/s and crashes into Earth

    • Before collision, has kinetic energy and little potential energy

    • Falls toward planet and speeds up

    • After collision, no kinetic energy or potential energy

    • Does the energy disappear? No, energy is transformed

    • Crater, Heat!

    • 1000 ton meteorite releases 5 x 10¹³ J. (1 kiloton TNT = 4.2 x 10¹² J, Hiroshima atomic bomb=6.3 x 10¹³ J)

V. Thermal equilibrium: heat flows to cooler regions

• Conduction: Heat transfer through atomic collisions (solid or liquid)

• Convection: Heat transfer by movement of masses of material (solid or liquid)

• Radiation: Heat transfer via transformation of light into motions of atoms and molecules