# 13.6 Entropy and the second law of thermodynamics: disorder and

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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.

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, ${Q}_{\text{c}}/{Q}_{\text{h}}={T}_{\text{c}}/{T}_{\text{h}}$ . Rearranging terms yields

$\frac{{Q}_{\text{c}}}{{T}_{\text{c}}}=\frac{{Q}_{\text{h}}}{{T}_{\text{h}}}$

for any reversible process. ${Q}_{\text{c}}$ and ${Q}_{\text{h}}$ are absolute values of the heat transfer at temperatures ${T}_{\text{c}}$ and ${T}_{\text{h}}$ , respectively. This ratio of $Q/T$ is defined to be the change in entropy     $\Delta S$ for a reversible process,

$\Delta S={\left(\frac{Q}{T}\right)}_{\text{rev}}\text{,}$

where $Q$ is the heat transfer, which is positive for heat transfer into and negative for heat transfer out of, and $T$ 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 $T$ to be the average temperature, avoiding the need to use integral calculus to find $\Delta S$ .

The definition of $\Delta S$ is strictly valid only for reversible processes, such as used in a Carnot engine. However, we can find $\Delta S$ precisely even for real, irreversible processes. The reason is that the entropy $S$ of a system, like internal energy $U$ , 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 $\Delta S$ 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 $\Delta S$ for that process. That will be the change in entropy for any process going from state 1 to state 2. (See [link] .)

what is the stm
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
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Rafiq
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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?
what king of growth are you checking .?
Renato
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?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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Bharti
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absolutely yes
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for teaching engĺish at school how nano technology help us
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NANO
how can I make nanorobot?
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what is fullerene does it is used to make bukky balls
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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
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