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Learning objectives

By the end of this section, you will be able to:

  • Define entropy.
  • 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.

The information presented in this section supports the following AP® learning objectives and science practices:

  • 7.B.2.1: The student is able to connect qualitatively the second law of thermodynamics in terms of the state function called entropy and how it (entropy) behaves in reversible and irreversible processes. (S.P. 7.1)
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] .)

Questions & Answers

Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
Alexia Reply
how would I work this problem
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
what is angular velocity
Obaapa Reply
Why does earth exert only a tiny downward pull?
Mya Reply
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
Obrian Reply
what is power?
aron Reply
power P = Work done per second W/ t. It means the more power, the stronger machine
e.g. heart Uses 2 W per beat.
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
Alona Reply
did you solve?
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
what do we call velocity
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
Kavita Reply
what about the wind vane
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
29/20 ? maybes
In what ways does physics affect the society both positively or negatively
Princewill Reply
Practice Key Terms 3

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