First law of thermodynamics
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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 heat in = work + change in internal energy: Q = W + U is different formulation of energy conservation for isolated system:

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First law of thermodynamics
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

    • heat in = work + change in internal energy: Q = W + U

    • 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” that is 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
HEAT ENGINES

  • 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: Unet = 0,  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:

    •  = W/Qin = W/ Qh = 1 - (Qc /Qh )


Heat engines and refrigerators
heat engines and refrigerators

  • engine

  • refrigerator


Carnot engine
CARNOT ENGINE

  • 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 Th, one at low temperature Tc;

    • 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:  = 1 - (Tc /Th) (note temperature here is measured in Kelvin)

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


Second 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.

  • consequence of 2nd law:

    • 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
ENTROPY

  • Entropy:

    • when heat Q at temperature T enters a system, the system's entropy S changes by S = Q/T

    • for the Carnot cycle: Qh taken from reservoir at temperature Th , Qc given to reservoir at temperature TcS = Qh/Th - Qc/Tc = 0, 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.


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