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  • Define entropy and calculate the increase of entropy in a system with reversible and irreversible processes.
  • Explain the expected fate of the universe in entropic terms.
  • Calculate the increasing disorder of a system.
Photograph shows a glass of a beverage with ice cubes and a straw, placed on a paper napkin on the table. There is a piece of sliced lemon at the edge of the glass. There is condensate around the outside surface of the glass, giving the appearance that the ice is melting.
The ice in this drink is slowly melting. Eventually the liquid will reach thermal equilibrium, as predicted by the second law of thermodynamics. (credit: Jon Sullivan, PDPhoto.org)

There is yet another way of expressing the second law of thermodynamics. This version relates to a concept called entropy    . By examining it, we shall see that the directions associated with the second law—heat transfer from hot to cold, for example—are related to the tendency in nature for systems to become disordered and for less energy to be available for use as work. The entropy of a system can in fact be shown to be a measure of its disorder and of the unavailability of energy to do work.

Making connections: entropy, energy, and work

Recall that the simple definition of energy is the ability to do work. Entropy is a measure of how much energy is not available to do work. Although all forms of energy are interconvertible, and all can be used to do work, it is not always possible, even in principle, to convert the entire available energy into work. That unavailable energy is of interest in thermodynamics, because the field of thermodynamics arose from efforts to convert heat to work.

We can see how entropy is defined by recalling our discussion of the Carnot engine. We noted that for a Carnot cycle, and hence for any reversible processes, Q c / Q h = T c / T h size 12{Q rSub { size 8{c} } /Q rSub { size 8{h} } =T rSub { size 8{c} } /T rSub { size 8{h} } } {} . Rearranging terms yields

Q c T c = Q h T h size 12{ { {Q rSub { size 8{c} } } over {T rSub { size 8{c} } } } = { {Q rSub { size 8{h} } } over {T rSub { size 8{h} } } } } {}

for any reversible process. Q c size 12{Q rSub { size 8{c} } } {} and Q h size 12{Q rSub { size 8{h} } } {} are absolute values of the heat transfer at temperatures T c size 12{T rSub { size 8{c} } } {} and T h size 12{T rSub { size 8{h} } } {} , respectively. This ratio of Q / T size 12{Q/T} {} is defined to be the change in entropy     Δ S size 12{ΔS} {} for a reversible process,

Δ S = Q T rev , size 12{DS= left ( { {Q} over {T} } right ) rSub { size 8{"rev"} } } {}

where Q size 12{Q} {} is the heat transfer, which is positive for heat transfer into and negative for heat transfer out of, and T size 12{T} {} is the absolute temperature at which the reversible process takes place. The SI unit for entropy is joules per kelvin (J/K). If temperature changes during the process, then it is usually a good approximation (for small changes in temperature) to take T size 12{T} {} to be the average temperature, avoiding the need to use integral calculus to find Δ S size 12{ΔS} {} .

The definition of Δ S size 12{ΔS} {} is strictly valid only for reversible processes, such as used in a Carnot engine. However, we can find Δ S size 12{ΔS} {} precisely even for real, irreversible processes. The reason is that the entropy S size 12{S} {} of a system, like internal energy U size 12{U} {} , depends only on the state of the system and not how it reached that condition. Entropy is a property of state. Thus the change in entropy Δ S size 12{ΔS} {} of a system between state 1 and state 2 is the same no matter how the change occurs. We just need to find or imagine a reversible process that takes us from state 1 to state 2 and calculate Δ S size 12{ΔS} {} for that process. That will be the change in entropy for any process going from state 1 to state 2. (See [link] .)

The diagram shows a schematic representation of a system that goes from state one with entropy S sub one to state two with entropy S sub two. The two states are shown as two circles drawn a distance apart. Two arrows represent two different processes to take the system from state one to state two. A straight arrow pointing from state one to state two shows a reversible process. The change in entropy for this process is given by delta S equals Q divided by T. The second process is marked as a curving arrow from state one to state two, showing an irreversible process. The change in entropy for this process is given by delta S sub irreversible equals delta S sub reversible equals S sub two minus S sub one.
When a system goes from state 1 to state 2, its entropy changes by the same amount Δ S size 12{ΔS} {} , whether a hypothetical reversible path is followed or a real irreversible path is taken.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics: physics of california. OpenStax CNX. Sep 30, 2013 Download for free at http://legacy.cnx.org/content/col11577/1.1
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