<< Chapter < Page Chapter >> Page >
  • 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

material that allows electric current to pass through
Deng Reply
material which don't allow electric current is called
Deng
insulators
Covenant
how to study physic and understand
Ewa Reply
what is conservative force with examples
Moses
what is work
Fredrick Reply
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
Esther Reply
difference between model and theory
Esther
Is the ship moving at a constant velocity?
Kamogelo Reply
The full note of modern physics
aluet Reply
introduction to applications of nuclear physics
aluet Reply
the explanation is not in full details
Moses Reply
I need more explanation or all about kinematics
Moses
yes
zephaniah
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
Muhammad Reply
yh
Isaac
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
Majok Reply
what is frontier of physics
Somto Reply
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Gufraan Reply
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
Ezekiel Reply
please explain
Samuel
what's the definition of physics
Mobolaji Reply
what is physics
Nangun Reply
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
Practice Key Terms 3

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask