Td Skct Unit 2.pptx

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UNIT 2 Second Law of Thermodynamics

Limitations of I Law 2



Does not specify the direction of flow of heat and work  i.e,

whether the heat flows from hot body to cold body or cold body to hot body.



Q and W are mutually convertible. W



– Converted fully to Q

This violates the foresaid statements.

Heat Engine 3







Device which extracts heat from a hot reservoir (source), converts it into useful work and a part of heat energy is rejected to a cold reservoir (sink). Heat source: (TERH) supplies heat continuously to the system operating in a cyclic process. Heat sink: (TERS) absorbs heat continuously from the system operating in a cyclic process.

Hot reservoir Q1=Qin

Energy intake

W=Qin-Qbody Working out

Q2=Qout

W = Qin - Qout

Energy exhaust

Cold reservoir

W Qin  Qout   Qin Qin

Refrigerator and Heat pump 4



Refrigerator  device

which extracts heat from a system to maintain its temperature lower than the surrounding.



Heat pump  device

which supplies heat to a system to maintain its temperature higher than the surrounding.

Hot reservoir Q2=Qout =Qin + W W=Qin-Qbody Working out

Qin = Q1 Cold reservoir

W

Performance of heat engines and reversed heat engines 5



Heat engine

where, 

W = Net work transfer from the engine, Q1= Heat transfer to engine. Refrigerator

where, 

Q2 = Heat transfer from cold reservoir, and W = Net work transfer to the refrigerator.

Heat Pump where,

Q1 = Heat transfer to hot reservoir, and W = Net work transfer to the heat pump.

Performance of heat engines and reversed heat engines 6

ηth is always less than unity and (C.O.P.) heat pump is always greater than unity. COP of heat pump = 1 + COP of refrigerator.

Statements of second law of thermodynamics 7

1. Kelvin-Planck Statement 2. Clausius Statement

Kelvin-Planck Statement  “It

is impossible to construct an engine, which while operating in a cycle produces no other effect except to extract heat from a single reservoir and do equivalent amount of work”.





It means that the efficiency of a heat engine cycle is never 100%. This precludes a perfect heat engine.

Statements of second law of thermodynamics 8

Clausius Statement  “It is impossible for a self acting machine working in a cyclic process unaided by any external agency, to convey heat from a body at a lower temperature to a body at a higher temperature”.  In other words, heat of, itself, cannot flow from a colder to a hotter body.  

This precludes a perfect refrigerator. Applies to refrigerators , air conditioners and heat pumps

Perpetual motion machine of the second kind (PMM- II) 9





Without violating the first law, a machine can be imagined which would continuously absorb heat from a single thermal reservoir and would convert this heat completely into work. The efficiency of such a machine would be 100 per cent.

Thermal Reservoir Q1 PMM2

W=Q1

Q2=0

Equivalence of the statements Violation of Kelvin-Planck Statement leads to violation of Clausisus statement T1 Q1 HE

Q1 + Q2 W=Q1

Q2=0

T1

HP

Q2

Equivalence of Clausius Statement to the KelvinPlanck Statement 11

T1 Q1 W=Q1 - Q2

Q1 = Q2

HE

HP Q2

Q2

T1

REVERSIBILITY AND IRREVERSIBILITY 12



Reversible or ideal process & Irreversible or natural process

y 

A

Reversible process System and surroundings restored to their initial states, without producing any changes in the rest of the universe.  Infinitely slow process  Consists of succession of equilibrium states 

B

x

Irreversible process 13





Thermodynamic equilibrium is not satisfied Dissipative effects are present 



Friction, viscosity, inelasticity, electrical resistance, magnetic hysterisis etc

y

A

B

Conditions for reversibility Equilibrium is attained  No dissipative effects  Quasi-static process 

x

Carnot cycle 14

Efficiency of the reversible heat engine 15

Carnot engine- Not possible 16

   

Isothermal process – Slow Adiabatic process – Fast Not possible to avoid friction b/w moving parts Heat source with const T is not possible

Carnot theorem 17



No engine operating on a cyclic process is more efficient than Carnot engine when working between same temperature limits. T1

Q1

HE andHE  R.HE 1

2

Q1 HE1

W

HE2

R.HE W’’

W’ Q2

Q’2

T1

Q1

Q’’2

Corollaries of Carnot Theorem 18





All the reversible engines operating b/w the two given TR with fixed temperature have the same efficiency ηR.HE operating b/w two reservoirs is independent of the nature of the working fluid and depends only on the T of the reservoirs

Clausius inequality 19



Whenever the closed system undergoes cyclic process, the algebraic sum of or cyclic integral of ratio of heat transfer to absolute temperature is always less than or equal to zero.

Or dQ  T 0

It provides a criterion for the reversibility of a cycle

Clausius inequality 20

We know that,

irrev  rev

 Q2   T2  1    1    Q1 irrev  T1  rev  Q2   T2          Q1 irrev  T1  rev When changing the sign, the equality changes

Q2 T2  Q1 T1

Q1 T1  Q2 T2

Q1 T1



Q2 T2

Q1 Q2 T1

Q1 T1





T2

Q2 T2

dQ  T 0 dQ  T 0 dQ  T 0

0 0

Rev. Cycle

Irrev. Cycle

Entropy 21

 



Index of unavailaibility or degradation of energy. Increases with the addition of heat and decreases with its removal. Mathematically, dS  dQ T 2 dS  2 dQ 1 1 T



Property of a system, depends only on end state of the process.

Principle of increase of entropy 22



    





For infinitesimal process, ds  dQ T For an isolated system, dQ = 0 Therefore dsiso  0 For a reversible process dsiso  0 or S = constant For an irreversible process dsiso  0 Proved that entropy of an isolated system can never decrease . It always increases and remains constant only when the process is reversible. This is known as the principle of increase of entropy or simply the entropy principle.

ENTROPY AND DIRECTION: THE SECOND LAW A DIRECTIONAL LAW OF NATURE 23



All spontaneous process or natural(irreversible process)  occur

only in one direction from a higher to a lower potential





Increase entropy of the Universe (system & surrounding) II law gives the direction of an increase in the entropy of the universe.

I and II law of TD summarised by Rudolf Clausius 24

 

The energy of the world (universe) is constant The entropy of the world tends towards a maximum.

III law of TD 

It is impossible by any procedure, no matter how idealized, to reduce any system to the absolute zero of temperature in a finite number of operations