Can anyone give me a formal definition of entropy and why is a bounday layer viewed as an entrophy hill.
Entropy can be defined as the measure of dissorder a system contains. One way to calculate entropy is to use a formula Ludwig Boltzman came up with:
S = k ln W
Where k is Boltzman's constant : k = 1.381 * 10-23 J/K
W represents the number of different ways in which energy of a system can be rearranged.
Entorpy deals with last two laws of thermodynamics and the Nernst Heat Theorem.
Second Law of Thermodynamics:
The entropy of an isolated system increases in the course of a spontaneous change:
Stot > 0
where Stot is the total entropy of the isolated system that contains the system of intrest.
Third Law of Thermodynamics:
If the entropy of every element in its most stable state at T=0 is taken as zero, then every substance has a positive entropy which at T=0 may become zero, and which does become zero for all perfect crystalline substances, including compounds.
Nernst heat theorem:
The entropy change accompanying any physical or chemical transformation approaches zero as the temperature approaches zero: as the temperature approaches zero the change in entropy approaches zero.
Here are some examples of entropy:
Why does a cold glass of lemonade become warm on a hot day? What is happening is a transfer of energy (heat) from the surroundings to the glass of lemonade. So that, the glass of lemonade increases in entropy (disorder, increased molecular movement) as the surrounding air decrease in entropy. The incease in entropy must equal the decrease in entropy.
How does an ice cube's melting deal with entropy? As an ice cube melts it changes states. To change state the ice cube's molecules must increase in activity. This increase is an increase in disorder or losely defined an increase in entropy.
Entropy is a tricky thing to define but maybe some of these links below will help give you a better grasp of this concept.
( definitions taken from Atkins, P. "Physical Chemistry 5th Ed.", 1994)
(1). Any introduction to engineering thermodynamics book or Physics book should have the definition of the entropy in it. Between two states (define a process), the entropy change is ds=delta_Q(the heat energy change)/T (the temperature). So, you can measure the temperature, the change in heat energy, and define the entropy difference. (2). For the idealized process, ds=delta_Q/T is the definition. For the real world process, it is shown that ds is greater than (delta_Q/T). (3). For flow processes, through the thermodynamic relationship, the Q,T can be related to the other varaiables, such as the total pressure of the fluid state. Thus, the mixing loss of the total pressure in the boundary can be expressed as the change in the entropy increase. That is, the entropy increase represent the total pressure loss, in the irreversible flow process. (4). It simply says "life is one way street". (the heat energy always flow from the high temperature to the low temperature state)
entropy increases in the viscous boundary layer due to viscous dissipation which is a necessarily irreversible process.
Entropy is property of the system.
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