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Chapter 5: The 2nd Law of Thermodynamics

An IntroductionThis 1000 hp engine photo is courtesy of Bugatti automobiles.

Motivating The 2nd Law of Thermodynamics

• The 1st law of thermodynamics alone does not predict the direction of a process, e.g.– Can a hot object naturally cool down to a temperature

below its surrounding?– Can a hot mass return to its initial position by losing

its internal energy?• The first law does not distinguish between

reversible and irreversible processes• The 2nd law can be used in conjunction with the

1st law to determine the capability (e.g., max efficiency) of a process.

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Spontaneous ProcessesObjects spontaneously tend to cool

Fluids move from higher to lower pressure environments spontaneously

Objects spontaneously fall from elevated positions

Spontaneous processes allows occur in a predictable direction, and have the potential to produce work

Comments• A spontaneous process takes place on its own

but its inverse would not take place spontaneously

• There is an opportunity to develop work from an spontaneous process that otherwise would be lost (e.g., turbine, pulley)

• If work is developed from s spontaneous process– What is the max theoretical limit– What factors would preclude its realization

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The Many Uses of the 2nd Law

• Predict process direction• Establish equilibrium conditions• Determine theoretical best performance• Evaluate factors limiting best performance• Define a temperature scale independent of

properties• Develop means for property evaluation for

derived properties, such as h and u

Statements of the 2nd Law

• Kelvin-Planck Statement• It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of energy by work to its surroundings while receiving energy from a single thermal reservoir

• Clausius Statement• It is impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from a cooler to a hotter body

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Proof Illustration

• K-P⇒Clausius • Clausius⇒K-P

Reversible vs. Irreversible• A process is called irreversible if the system and

all parts of its surroundings cannot be exactly restored to their initial values

• A Process is reversible if both the system and surroundings can be returned to its initial states.

• An irreversible process may be returned to initial state but not if combined with surroundings

• All real-world processes are irreversible

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Irreversibilities• Heat transfer through a finite temperature

difference• Unrestrained expansion of a gas or liquid• Spontaneous chemical reaction• Spontaneous mixing• Friction (sliding and flow)• Electric current flow through a resistance• Magnetization or polarization with hysteresis• Inelastic deformation• And many more …

ClipArt courtesy of PowerPoint 2002

ClipArt courtesy of PowerPoint 2002

ClipArt courtesy of PowerPoint 2002

Internal vs. External Irreversibilities

• For engineering analyses the internalirreversibilities may be considered as opposed to total.

• A process is internally reversible if there are no internal irreversibilities

• An internally reversible process can return to its initial state

• It consists of a series equilibrium states, i.e., quasiequilibrium prcocess

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How to Prove Irreversibility

• The proof is typically by contradiction• First suppose the process is reversible• Put together a series of additional

reversible (ideal) processes to form a thermodynamic cycle

• Show that existence of such a cycle would violate the Kevin-Planck Statement

• Example: Heating due to Friction

Example: Irreversibility of Friction

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Examples of Reversible Processes

• Frictionless mass-spring or pendulum• Adiabatic expansion or compression in

friction-less piston cylinder• Statble equilibrium states

Power Cycles (Heat Engines)

1cycle L

H H

W QQ Q

η = = −

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Refrigeration and Heat Pump Cycles

Refrigeration Heat Pumps

C C

cycle H C

Q QW Q Q

β = =−

H H

cycle H C

Q QW Q Q

γ = =−

Carnot Corollaries

• The thermal efficiency of an irreversible power cycle is always less than that of a reversible one when each operates between the same two reservoirs.

• All reversible power cycles between the same two thermal reservoirs have the same thermal efficiency.

• There are similar corollaries for refrigeration and heat pump cycles.

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Proof Of Carnot Corollary

Kelvin Scale

• Carnot corollaries imply that for a reversible power cycle Qc/QH= ψ(Tc,TH)– Qc: Heat from system to cold reservoir– QH: Heat from hot reservoir to system– Tc,TH: cold and hot reservoir temperature– ψ: unspecified function

• Kelvin scale: ψ(Tc,TH)=Tc/TH

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The Kelvin Temperature Scale

C C

H Hrev

Q TQ T

⎛ ⎞=⎜ ⎟

⎝ ⎠

273.16revHcycle

QTQ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

273.16 K is the Triple Point temperature of waterClipArt courtesy of PowerPoint 2002

Maximum Performance

max 1 C

H

TT

η = −

Heat Engines Refrigerators & Heat Pumps

maxC

H C

TT T

β =−

maxH

H C

TT T

γ =−

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Carnot CycleReversible power cycle: Two adiabatic processes

alternated with two isothermal processes

Carnot power cycles operated in reverse may be regarded as a reversible refrigeration or heat pump cycle, with maximum coefficient of

performance

Example: Problem 5.38

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Problem 5.40

Problem 5.50