29 March 2011

Laws of Thermodynamics

First Law of Thermodynamics :
The increase in internal energy as a result of heat absorbed is diminished by the amount of work done on the surroundings:
dEi = dq - dw = dq - PdV
By convention, heat added to the system, dq, is positive and work done by the system, dw, on its surroundings is negative.

This is also called the Law of Conservation of Energy.

Definition of Enthalpy :

We can define a new state variable (one where the path to its current state does not affect its value) called enthalpy:

H = Ei + PV

Enthalpy =  Internal Energy  +  PV

Upon differentiation and combing with our earlier definition for internal energy:

dH = dEi + PdV + VdP
 
dEi = dq - PdV

dH  =  dq  +  VdP

Enthalpy, Melting, and Heat :

For isobaric (constant pressure) systems, dP = 0 and then the change in enthalpy is equal to the change in heat: dHp  =  dqp

Three possible changes in a system may occur:

  1) Chemical reactions (heterogeneous)
  2) Change in state (e.g. melting)
  3) Change in T with no state change

Heat capacity is defined by the amount of heat that may be absorbed as a result of temperture change at constant pressure:

Cp = (dH/dT)p

Second Law of Thermodynamics :

One statement defining the second law is that a spontaneous natural processes tend to even out the energy gradients in a isolated system.
Can be quantified based on the entropy of the system, S, such that S is at a maximum when energy is most uniform.  Can also be viewed as a measure of disorder.
  
DS  = Sfinal  -  Sinitial  > 0
 
 
Third Law Entropies:

All crystals become increasingly ordered as absolute zero is approached (0K = -273.15°C) and at 0K all atoms are fixed in space so that entropy is zero.