Understanding Entropy: Exploring the Concept of Qrev/T

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In summary, the First Law of Thermodynamics states that the differential change in energy equals the heat transferred to a system plus the work done on a system.
  • #1
aniketp
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Hey can neone tell me why this is so? I have not got the ans in any book i read...
Thnx 4 replying
 
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  • #2
Hi aniketp,

One way of writing the First Law is

[tex]dU=q+w[/tex]

which means that the differential change in energy equals the heat transferred to a system plus the work done on a system. But another way is

[tex]dU=T\,dS-p\,dV[/tex]

where the work is expressed as a generalized force (pressure) times a generalized displacement (change in volume). The heat transfer term is expressed in an analogous way: a generalized force (temperature) times a generalized displacement (change in entropy).

If you haven't heard the terms generalized force and generalized displacement before, they're just ways to classify variables. Generalized forces are intensive, and they drive processes; a change in temperature drives heat flow, and a change in pressure drives mass flow. Generalized displacements, which are extensive, are the "stuff" that is transferred: entropy, volume.

[itex]S=Q_\mathrm{rev}/T[/itex] arises because at constant volume and temperature, and if the process is reversible (no excess entropy generated) we can integrate [itex]q=T\,dS[/itex] to give [itex]Q_\mathrm{rev}=T\Delta S[/itex].

Does this make sense?
 
  • #3
Hey mapes,
But isn't dU=TdS-PdV actually derived from dS=dQ/T?
 
  • #4
No...

Entropy is defined as S = k*log(omega)
Temperature is defined as 1/T = dS/dU at constant V
Pressure is given by P = T * dS/dV at constant U

From the previous two relationships it follows that
dU = TdS - PdV, and S = Q/T is a special case.

For an intuitive discussion see, for example, An Introduction to Thermal Physics by Schroeder, sections 2&3.
 
  • #5
I should mention that these expressions for T and P are derived (in Schroeder) by consideration of equilibrium conditions.
 
  • #6
Hi nicksauce, thnx 4 the help. So T & P are actually defined on the basis of entropy...
But in k*log(omega) what do 'k' n 'omega represent?
 
  • #7
k is the Boltzmann constant, and omega is the "multiplicity" of the system, or the number of possible microscopic configurations the system can have.

Simple example:
Say I have a system of 3 "oscillators" (that are quantized), with a total energy of "q" units. Say q = 0, then there is only one possible arrangement (Omega=1). Say q = 1, then there are three possible arrangements (Omega = 2). Say q =2, then there are 6 possible arrangements, ie (2,0,0) three times, and (1,1,0) 3 times. So Omega = 6. Say q = 3, then there are 10 possible arrangements, (3,0,0) 3 times, (2,1,0) 6 times, and (1,1,1) once. So Omega = 10.
 
  • #8
Oh ,ok. got it now...thanks once more !
 
  • #9
http://en.wikipedia.org/wiki/Fundamental_thermodynamic_relation" [Broken]
 
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1. What is entropy?

Entropy is a physical quantity that measures the level of disorder or randomness in a system. In simple terms, it is a measure of how much the energy in a system is spread out or distributed.

2. What is the relationship between entropy and temperature?

The relationship between entropy and temperature can be described by the equation Qrev/T, where Qrev is the reversible heat transfer and T is the temperature. This equation shows that as temperature increases, the entropy of a system also increases.

3. How does entropy affect the behavior of a system?

Entropy affects the behavior of a system by determining the direction of spontaneous processes. A system will naturally tend towards a state of higher entropy, meaning a state of greater disorder or randomness.

4. Can entropy ever decrease?

In isolated systems, the entropy can never decrease. This is known as the second law of thermodynamics. However, in open systems, where energy can be exchanged with the surroundings, entropy can decrease locally as long as it is compensated for by an increase in entropy in the surroundings.

5. How is the concept of entropy used in different fields of science?

The concept of entropy is used in various fields of science, including thermodynamics, statistical mechanics, information theory, and chemistry. It is a fundamental concept that helps us understand and predict the behavior of systems at a microscopic level.

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