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In a heat engine, the temperature difference between

the hot region and the cold region is the measure of the

available energy.

However, the second law states that, in an isolated

system heat must flow from a hot region to a cold.

With time, therefore, this temperature difference mustdecrease, for as the heat flows in the only direction it canflow, the hot region cools down and the cold region

warms up.

Consequently, the available energy decreases with

time. Since the total energy remains constant, the

unavailable energy must increase as the availableenergy decreases.

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If an ideal frictionless reversible engine removes

Qh from some substance at Th, does some work,and delivers Qc to some other substance at Tc, then

Qh/Qc = Th/ Tc

or

Qh/ Th = Qc/ Tc.

Clausiusused the last expression to introduce

entropy, S.

Entropy

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Definition: Consider any infinitesimal process in

which a system changes from one equilibrium stateto another. If dQris the amount of energy transferred

by heat when the system follows the reversible path

between the states, then the change in en tropy dSis

equal to this amount of energy for the reversible

process divided by the absolute temperature of the

system, T:

dS= dQr/TThe temperature is assumed constant because the

process is infinitesimal.

Entropy has units of Joules per Kelvin [J/K]

Entropy

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alculating entropy always use temperature in

elvin!

onsider a system in two different conditions, for

xample 1 kg of ice at 0oC, which melts and turns into

1 kg of water at 0oC. We associate the entropy withach condition.

he entropy of any substance is a function of the

ondition of the substance.

or an ideal gas it is a function of its temperature and

olume, and for a solid and liquid it is a function of its

Entropy

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The entropy is independent of the past history of the

substance. The entropy of the 1 kg of water at 0o

C is thesame if we obtained the water from ice, or if we cooled the

water from room temperature down to 0oC.

Entropy is a state function (as temperature and internal

energy) because the change in entropy does not depend on

the path followed.

Sign:

When the energy is absorbed by the system, change in theheat is positive and the entropy of the system increases.

When energy is expelled by the system, dQris negative, and

the entropy of the system decreases.

Entropy

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To calculate the change in entropy for afinite process we need to integrate the energy

transferred by heat divided by the temperature

(which is not constant) along a reversiblepath:

S = =f

i

f

i TdQrdS

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In Carno-engine, the entropy of the substance at Thdecreases by Qh / Th and the entropy of thesubstance at Tc increases by the same amount.

There is no net change in entropy, if we consider

the entire system.

But a real engine always delivers more heat at Tcthan a reversible engine. For a real engine Qc / Tcis always greater than Qh / Th.

The entropy of the substance at Th decreases, but

the entropy of the substance at Tc increases by a

larger amount. The entropy of the whole system

increases.

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The total entropy of an isolated system is always

increasing is another way of stating the second lawof thermodynamics.

A closed system is a system that does not interact in

any way with its surroundings. In practice there arereally no closed isolated systems except, perhaps,

the universe as a whole.

Therefore we state the second law in the following

way: The total entropy of the universe is always

increasing.

Entropy

Entrop in thermal processes meas res the e tent to hich

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Entropy in thermal processes measures the extent to which

energy of a system is available for conversion to work.

If a system undergoing an infinitesimal reversible change takes

in a quantity of heat dQ at absolute temperature T, its entropy is

increased by:

dS = dQ r/T

The area under the absolute temperature-entropy graph for a

reversible process represents the heat transferred in the process.S

T

Q

For an adiabatic process, there is no heat transfer and the

temperature-entropy graph is a straight line, the entropy remainingconstant throu h the rocess.

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The first law of thermodynamics says that the total quantityof energy in

the universe remains constant. This is the principle of the conservation of

energy.

The second law of thermodynamics states that the qualityof this energyis degraded irreversibly. This is the principle of the degradation of

energy.

The first principle establishes the equivalence of the different forms of

energy (radiant, chemical, physical, electrical, and thermal), the possibilityof transformation from one form to another and the laws that govern these

transformations.

Physical, chemical, and electrical energy can be completely changed into

heat. But the reverse (heat into physical energy, for example) cannot befully accomplished without outside help or without an inevitable loss of

energy in the form of irretrievable heat.

This does not mean that the energy is destroyed; it means that it

becomes unavailable for producing work.

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More About Change in Entropy

dQris measured along a reversible path,even if the system may have followed an

irreversible path

The meaningful quantity is the change inentropy and not the entropy itself

For a finite process,

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Change in Entropy

The change in entropy of a system

going from one state to another has the

same value for all paths connecting the

two states

The finite change in entropy depends only

on the properties of the initial and final

equilibrium states

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S for a Reversible Cycle

S= 0 for any reversible cycle

In general,

This integral symbol indicates the integral isover a closed path

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S for a Quasi-Static, Reversible Process

Assume an ideal gas undergoes a quasi-static, reversible process

Its initial state has Tiand Vi Its final state has T

fand V

f The change in entropy is

This demonstrates that Sdepends on onlythe initial and final states and not the pathbetween the states

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Entropy and Heat

The change in entropy depends only on theendpoints and is independent of the pathfollowed

The entropy change for an irreversibleprocess can be determined by calculating

the change in entropy for a reversibleprocess that connects the same initial andfinal points

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ntropy Changes in Irreversible Processe

To calculate the change in entropy in a realsystem, remember that entropy dependsonly on the state of the system

Do not use Q, the actual energy transfer inthe process Distinguish this from Qr, the amount of energy

that would have been transferred by heat alongreversible path

Qr is the correct value to use for S

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If the process is irreversible, then the totalentropy of an isolated system alwaysincreases

In a reversible process, the total entropy of anisolated system remains constant

The change in entropy of the Universe

must be greater than zero for anirreversible process and equal to zero for areversible process

ntropy Changes in Irreversible Processe

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Heat Death of the Universe

Ultimately, the entropy of the Universe shouldreach a maximum value

At this value, the Universe will be in a state of

uniform temperature and density All physical, chemical, and biological processes

will cease

The state of perfect disorder implies that no energy isavailable for doing work

This state is called the heat death of the Universe

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S in Thermal Conduction

The cold reservoir absorbs Q and its entropyincreases by Q/Tc

At the same time, the hot reservoir loses Q andits entropy decreases by -Q/T

h Since Th > Tc, the increase in entropy in the cold

reservoir is greater than the decrease in entropyin the hot reservoir

Therefore, SU> 0 For the system and the Universe

Adi b i F E i

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Adiabatic Free Expansion

This is an example of adiabaticfree expansion

The process is adiabatic becauseit takes place in an insulatedcontainer

Because the gas expands into avacuum, it does not apply a forceon a piston and W= 0

Since Q = 0 and W= 0, Eint = 0and the initial and final states arethe same No change in temperature is

expected

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S in a Free Expansion

Consider an adiabatic free expansion

Q = 0 but cannot be used since that is for

an irreversible process

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S in Free Expansion

For an isothermal process, this becomes

?S = nRln(Vf

/Vi

)

Since Vf> Vi , S is positive

This indicates that both the entropy andthe disorder of the gas increase as a resultof the irreversible adiabatic expansion

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S in Calorimetric Processes

The process is irreversible because the systemgoes through a series of nonequilibrium states

Assuming the specific heats remain constantand no mixing takes place:

If mixing takes place, this result applies only to

identical substancesS will be positive and the entropy of the Universe

increases

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