THERMODYNAMICS

• thermodynamics (from Greek therme = heat, dynamis = strength, power) = branch of physics dealing with energy transformations from and into thermal energy;
• mechanics:
  mechanical (external) energies of systems, governed by Newton's laws;
• thermodynamics:
  internal energy of systems and its relation to work
• keywords of thermodynamics:
  temperature, heat, internal/thermal energy, entropy
• four laws of thermodynamics:
  • heat transfer, thermal equilibrium
  • energy conservation
  • not all thermal energy is useful
  • impossility to reach absolute zero temperature
• topics to be discussed:
  • thermal energy, temperature, heat
  • 0th law
  • temperature scales
  • thermal expansion
  • heat capacity, specific heat
  • heat transfer: conduction, convection, radiation
  • 1st law
  • heat engines, efficiency
  • 2nd law
  • entropy

thermal energy, temperature, heat

• Brownian motion:
  Robert Brown observed burlap seeds dancing in water (1827);
  explained by A. Einstein (1905); calculated mean net disatnce travelled by random motion
  experimental verification by Jean Perrin (1908).
• thermal motion:
  disorganized random motion of constituent atoms and molecules within body of matter;
• thermal energy:
  kinetic energy of thermal motion (translational, rotational, vibrational) associated with ensemble of particles;
  (note Leibniz (1695): seeming loss of "vis viva" in inelastic collisions is only apparent, vis viva not destroyed, but dissipated among the parts)
• temperature:
  is measure of average value of thermal energy of atoms and molecules (not total amount of thermal energy);
  (temperature of a substance is independent of total number of atoms/molecules)
  is a measure of the ability of randomly moving particles to impart thermal energy to a thermometer;
• heat = thermal energy transferred from a region of high temperature to region of lower temperature;
  body stores thermal energy ("internal energy");
  heat = thermal energy "in transit"

• 0th law of thermodynamics:
  • between bodies of different temperature (i.e. of different average internal thermal energy), heat will flow from the body of higher temperature to the body of lower temperataure until the temperatures of the two bodies are the same; then the bodies are in "thermal equilibrium"
  • two bodies are in thermal equilibrium (at same temperature) if there is no heat flow between them;
  • corollary: if two bodies are in thermal equilibrium with a third body, then they are in thermal equilibrium with each other. can use thermometer to compare temperature
  • note:
    observation only shows that temperatures equalize - heat flow is hypothesis

TEMPERATURE SCALES

• temperature was measured long before it was understood;
• Galilei (around 1592): "device to measure degree of hotness"; inverted narrow-necked flask, warmed in hand, put upside down into liquid; liquid level indicates temperature; OK, but not calibrated.
• Hooke, Huygens, Boyle (1665): "fixed points" - freezing or boiling point of water;
• Carlo Renaldini (1693): use both freezing and boiling point.
• Fahrenheit scale
  Gabriel Daniel Fahrenheit (Danzig, 1686-1736),
  glassblower and physicist;
  first really operational and reproducible thermometer using mercury (liquid throughout range) (1714)
  0 point: lowest temperature of winter of 1709,
  (using mix of water, ice, salt)
  = body temperature (96 divisible by 12, 8)
  water freezes at F, boils at F
• Celsius scale
  Anders Celsius (Swedish astronomer, 1701 - 1744)
  C = ice point (mixture of water and ice at 1 atm)
  C = boiling point of water at 1 atm. (1742)
  relation between Fahrenheit and Celsius degrees:

  

• thermodynamic temperature scale
  (absolute, Kelvin scale)
  pressure vs temperature of gas at constant volume, and volume vs temperature of gas at constant pressure extrapolate to zero at
  this is "absolute zero"
  unit: Kelvin

Range of temperatures

• highest temperature: in core of stars, K seems maximum;
• hydrogen bomb ignites at K;
• interior of Sun K;
• plasma K;
• K: clouds of atoms, ions, e, occasional molecule;
• 5800 K: surface of the Sun;
• 5000 K: cool spots at surface of the Sun; evidence for some molecules;
• 3000 K: water steam: about 1/4 of water molecules ruptured into atoms;
• 2800 K: W light bulb filament;
• 2000 K: molten lava;
• 1520 deg. C: iron melts;
• 327 deg C: lead melts;
• 100 deg C (373 K): water boils
• 252 K: temp. of salt-ice mix;
• 234 K: mercury freezes
• 194 K: dry ice freezes;
• 77 K: nitrogen boils
• 4 K: helium boils.

THERMAL EXPANSION

• solids, liquids and gases expand when heated
• knowledge about this is old: e.g. red-hot iron rims put on wagon wheels;
• thermometers ar based on this;
• heating internal energy rises vibrations have larger amplitude, equilibrium positions move farther apart.
• typical metal expands by about 7% between 0 K and melting point.

  

  = coefficient of thermal expansion;

• examples:
  

  

• have to account for this in construction
  e.g. expansion joints at end of bridge, gaps in rails;
  also in dental fillings
• uses: thermostats, thermometers (bimetal strips)
• anomaly of water:
  maximum of density at 4 deg C.

HEAT CAPACITY

=
measure of ability of a substance to absorb thermal energy;

• specific heat capacity = heat capacity per unit mass;

  

  Q = amount of thermal energy added,
  c = specific heat capacity,
  = raise in temperature;

• 1 calorie = 1 cal ( = 4.186 J)
  = thermal energy necessary to raise temperature of 1 gram of water by 1 degree Celsius (from );
• 1 kcal = 1 Cal
  = thermal energy necessary to raise temperature of 1 kilogram of water by 1 degree Celsius (from );
  called ``calorie'' in nutrition;
• water has high specific heat capacity
  moderating influence on climate

  

HEAT TRANSFER

• conduction
  = heat transfer by atomic/molecular collisions;
  • thermal conductivity = ability of substance to transmit heat, depends on atomic/molecular structur;
  • metals typically 400 times better than other solids;
  • most solids little better than liquids;
  • liquids about 10 times better than gases
  • good heat conductor ususally good electric conductor

• convection
  = heat transfer by motion of hot matter
  • change of density of fluid (liquid or gas) due to heating
    flow of fluid up, away from heat source;
  • dominant mechanism for many heat loss processes in air;
  • examples: household radiator, hurricanes
  • purpose of fur, feathers, clothing, blankets: prevent convection
  • "chill-factor"
• radiation
  = heat transfer
  by emission and absorption of electromagetic radiation;
  e.g. Earth receives by radiation from the Sun

FIRST LAW OF THERMODYNAMICS

• first law of thermodynamics:
  heat added to a system goes into the internal energy of the system and/or into doing work
  

  

  

• is different formulation of energy conservation
• for isolated system:
  no heat flow, if work done, must reduce internal energy

• historical note:
  1st law quoted as a law in its own right because it took a long time to realize that heat is a form of energy. Until around 1800, heat was considered a ``fluid'' called "caloric" contained in materials, can be soaked up by materials,..
  It took about 50 years to replace this with the new paradigm that heat is a form of energy,
  and that total energy, including thermal energy, is conserved.
  Milestones on path to first law:
  Experiments and observations by Benjamin Thompson, James Prescott Joule, Julius Robert Mayer,.. and conjectures by Mayer, Hermann Helmholtz, Rudolf Clausius,..

HEAT ENGINES

• a heat engine is a device that converts heat into work
• principle: heat input, some of it used to do work, some of it discarded
• operate in cyclical process, i.e. at end of an "engine cycle", engine must be in same state as before
  
• for a cyclical process: Q = W
  i.e. work done = net heat input = (heat in) - (heat out)

  

• heat engine operates between two "reservoirs";
  reservoir = system from which heat may be readily extracted and into which heat can be deposited at given temperature
• heat engine takes heat from high temperature reservoir, converts some of it into work, and ejects rest of heat into low temperature reservoir;
• example: car engine:
  hot reservoir = cylinder in which air-fuel mixture is exploded;
  cold reservoir = environment to which waste heat is expelled;
• thermal efficiency of a heat engine =
  ratio of work output to heat input:

  

  

CARNOT CYCLE

• Nicolas Léonard Sadi Carnot (1796 - 1832)
  ("Réflexions sur la puissance motive de la chaleur", 1824)
  constructed idealized method for extracting work with greatest possible efficiency from an engine with heat-flow from one substance at higher temperature to another substance at lower temperature,
  

  - the "Carnot cycle"

• Carnot cycle is reversible process - can run in either direction
• Carnot engine:
  • container with piston
  • can be brought into thermal equilibrium with two heat reservoirs, one at high temperature , one at low temperature ,
  • or can be isolated from outside world
    (i.e. no heat-flow to or from container);
  • isothermal process: temperature constant;
  • adiabatic process: isolated no heat exchange;
  • efficiency of Carnot engine:
    for Carnot engine,

    

    (note temperature here is measured in Kelvin)

• Carnot engine is the most efficient engine possible
  (2nd law of thermodynamics).

SECOND LAW OF THERMODYNAMICS

• several different formulations of 2nd law;
  all can be shown to be equivalent:
  • "law of heat flow:"
    Heat (thermal energy) flows spontaneously (i.e. without external help) from region of higher temperature to region of lower temperature. By itself, heat will not flow from cold to hot body.
  • Kelvin formulation:
    No process is possible whose sole result is the removal of heat from a source and its complete transformation into work.
  • Clausius formulation:
    No process is possible whose sole result is the transfer of thermal energy from a body at low temperature to a body at high temperature.
  • heat engine formulation:
    No heat engine can be more efficient than the Carnot engine.
• the quality of thermal energy (its ability to do work) depends on the temperature;
  thermal energy at low temperature less useful than thermal energy at high temperature;
• "using energy" does not mean destroying it (cannot be destroyed);
  it means converting it into work and thermal energy at lower temperature than before
  "degradation of energy"

ENTROPY

• Rudolf Clausius (1865):
  when heat Q at temperature T enters a system, the system's entropy S changes by

  

• for the Carnot cycle: taken from reservoir at temperature ,
  given to reservoir at temperature

  

  

  i.e. for the Carnot cycle, the change in entropy is = 0.

• for other cyclical processes: 2nd law of thermodynamics
  efficiency smaller than that of Carnot process

  

• entropy formulation of 2nd law of thermodynamics:
  For any process, the total entropy of all the participants either increases or stays the same; it cannot decrease.
• entropy related to the degree of disorder, to the probability of a state;
• order is less probable than disorder (there are many more ways of having disorder than there are of having order);
• some systems (e.g. living things and beings) decrease their entropy, but at the cost of increasing the entropy of the rest of the universe.
• The total entropy of the universe keeps increasing.