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Three Laws of Thermodynamics

  1. The first law of thermodynamics says that you can't win the game; the best you can hope for is a tie (conservation of energy).
  2. The second law of thermodynamics says that a tie is only possible at absolute zero (the entropy of the universe is always increasing except at absolute zero).
  3. The third law of thermodynamics says that you'll never achieve absolute zero (a system will asymptotically approach an entropy minimum as it asymptotically approaches absolute zero).


Zeroth Law of Thermodynamics

based on a simple observation:

When one object is in thermal equilibrium with another object, and the second object is in thermal equilibrium with a third object, then the first and third object are also in thermal equilibrium and when brought into thermal contact (which doesn't necessarily imply physical contact, by the way), no net heat will flow between them.


thermal equilibrium 

no net heat flows between objects in thermal equilibrium 


 thermal expansion 

amount of length change is proportional to the original length of the solid and the increase in temperature:

ΔL=αLΔ T  


  • where Δ L is the change in length, 
  • L is the original length, and
  • Δ T is the change in temperature. 
  • coefficient of linear expansion α is a constant that characterizes how a specific material's length changes as the temperature changes


volume expansion.

Δ V = ßVΔT

formula for volumetric thermal expansion is applicable to both liquids and solids:

Δ V is the change in volume, V is original volume, ß=3(alpha)=coefficient of volume expansion, T=temperature



first law of thermodynamics

  •  Δ U is the change in the system's internal energy, 
  • Q is the energy transferred through heat to the system, and 
  • W is the work done by the system.

the first law states that the change in the total internal energy of a system is equal to the amount of energy transferred in the form of heat to the system, minus the amount of energy transferred from the system in the form of work.

The internal energy of a system can be increased by adding heat, doing work on the system, or some combination of both processes. 


sign convention

work done by the system is positive, while work done on the system is negative; heat flow into the system is positive, while heat flow out of the system is negative. 


second law of thermodynamics:

Objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature (and come to thermal equilibrium).



process by which a quantity of energy is transferred between two objects as a result of a difference in temperature


(heat can never spontaneously transfer energy from a cooler object to a warmer one without work being done on the system)


SI Unit for Heat

Joule (J)



Three means by which heat can transfer energy

conduction, convection, and radiation



direct transfer of energy from molecule to molecule through molecular collisions

  • must be direct physical contact between the objects
  • Best: metals ("sea of electrons"
  • Worst: Gases (lots of space btwn individual molecules



 transfer of heat by the physical motion (flow) of the heated material

  • involves flow: fluids (liquids and gases) can transfer heat by this means
  • heated portions of the fluid rise from the heat source, while colder portions sink (because density decreases as temperature increases)
  • convection ovens are more efficient and produce better results




transfer of energy by electromagnetic waves

  • can travel through a vacuum
  • radiant ovens: hot metal box  radiates the energy through the open space of the oven where it is absorbed by the food


specific heat (c)

the amount of heat energy required to raise 1 kg of a substance by 1° C or 1 K.

  • specific heat for a substance changes according to its phase
  • specific heat of liquid water: 1,000 calories per 1 kilogram per 1° C or 1 K.
  • Equivalently, this can be expressed as 4,184 joules per 1 kilogram per 1° C or 1 K.
  • specific heat for liquid water is greater than that of either ice or steam. This means that more energy per unit mass must be delivered to the liquid water to raise its temperature by one degree


Heat of Transformation


  • where Q is the amount of heat gained or lost, m is the mass of the substance, and L is the heat of transformation of the substance
  • phase changes occur at constant temperature, and the temperature will not begin to change until all of the substance has been converted from one phase into the other.
  •  phase changes are related to changes in potential energy, not kinetic energy


heat of fusion

phase change from liquid to gas (vaporization) or gas to liquid (condensation) occurs at the boiling point


heat of vaporization

phase change from liquid to solid (freezing) or solid to liquid (melting or fusion) occurs at the melting point.


Setup: Approximately how much heat is req to completely melt a 1 kg silver chain whose initial temp is 20 deg C?

Qtotal = Qbring to boiling pt + Qheat of transformation

Qtotal = mc ΔT + mL

  • m=mass
  • c=specific heat of silver
  • ΔT=(melting point - initial temperature)
  • L=heat of fusion


Work in a Gas System

(piston cylinder)

  • when is work done? (ie: how do you know?
  • when is work positive?
  • when is work negative?

  • Work has been done if volume of system has changed due to an applied pressure
  • gas expands (+W)→pushes up against the piston→exerts force (F = PA), → piston to moves up →volume of the system increases.
  • gas is compressed (-W): piston pushes down on the gas→exert a force (F = PA)→the volume of the system decreases. 


Work is pathway dependent

  • Calculate the work done on or by a system by finding the area under the pressure-volume curve.
  • V constant, with  ΔP : then no work is done (because there is no area to calculate.) 
  • P constant , with  ΔV:  the area under the curve is a rectangle of length P and width Δ V (Vf− Vi). Work is as follows: 


What work is done when decrease in pressure from P1 to P2 at a constant volume?


no change in volume, the work done in this process is zero.



What work is done when system expands from V1 to V2 at a constant pressure?

isobaric process

(+)W = PΔ V.

Because the gas has expanded, the work was done by the gas and is positive. 


What work is done when neither pressure nor volume is held constant?

graphical analysis (fig C): The total area under the graph (Regions I and II) gives the work done

  • The work done is the sum of the areas of regions I and II:

W=A1 + A2

  • Region I is a triangle whose base is Δ V and whose height is Δ P, so the area is

  • Region II is a rectangle with base Δ V and height P2, so its area is


What work is done in a closed cycle in which, after certain interchanges of work and heat, the system returns to its initial state?

Because work is positive when the gas expands and negative when the gas is compressed, the work done is the area enclosed by the curve.


three particular thermodynamic processes as special cases of the first law

  • isovolumetric, isochoric; (constant volume),Q=0; ΔU=Q
  • adiabatic (no heat exchange): W=0; ΔU= -W
  • closed cycle, isothermal,  (constant internal energy, return to initial state), ΔU=0, Q=W


second law of thermodynamics

Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so



measure of the spontaneous dispersal of energy at a specific temperature

how much energy is spread out or how widely spread out energy becomes in a process


Reversible process

  • Net change in entropy of the system and its surroundings is zero

where L is the latent heat (either heat of fusion or heat of vaporization), m is mass, and T is the constant temperature of the system and environment in Kelvin.

  • No real processes are reversible but we can approximate reversibility:
  • Make sure the process goes slowly (infinate amt of time) and is always in equilibrium.
  • Ie: melting and refreezing ice is not a physics def of reversible, bc are changing conditions (is not spontaneous either way under one set of conditions--doesn't freeze at room temp)



Essential equations: Thermodynamics