CHAPTER-20

Entropy and Second Law of Thermodynamics

CHAPTER-20 Entropy and Second Law of Thermodynamics

1. Topics to be covered:2. Reversible processes3. Entropy4. The Carnot engine5. Refrigerators6. Real engines

Ch 20-2 Irreversible Process and Entropy

Irreversible Process: One way process If the irreversible process proceed in a closed system in

a reverse way, we will wonder about it. A melted piece of ice freezes by itself. Although from energy conservation, the process can proceed in the reverse path i.e.heat released in in the environment in melting ice can be recovered back into ice piece to solidify it . Energy conservation does not prohibit the process to proceed one way or the reverse way.

Which parameter the one ay direction of the process?. Entropy set the direction of irreversible process and

irreversible process proceed through that path in which entropy of the system always increases

Entropy Postulate: If an irreversible process occurs in a closed system, the entropy S of the system always increases

Change in entropy: (The arrow of time)-time reversal impossible due to entropy violation

Entropy definition: Two methods:

i) Using system’s temperature and heat loss/gain by the system

ii) By counting the ways in which the atoms or molecules of the system can be arranged

iii) Entropy S: state property like P,V,T, S

iv) Change in entropy S=Q/Tv) S=Sf-Si=f

i Q/T

Ch 20-2 Irreversible Process and Entropy

Free Expansion of an ideal gas- Irreversible Process:

An ideal gas expands from i to f state in an adiabatic process such that no work is done on or by the gas and no change in the internal energy of the system i.e. Ti=Tf; piVi=pfVf ;W=Eint=0

S=Sf-Si=fi Q/T

Integral from i to f cannot be solved for an irreversible process but can be solved for a reversible process.

Since S is state variable (Sif)rev= (Sif)irrevSirrev= Srev= Sf-Si= f

i Q/T (irreversible)To find the entropy change for an

irreversible process in a closed system, replace that process with any reversible process that connects that connects same initial and final states and calculate its change in entropy

Ch 20-3 Change in Entropy

Ch 20-3 Change in Entropy

Calculation of Entropy in Reversible Process

In free expansion Ti=Tf, i.e. isothermal process then reversible isothermal expansion process can be used to calculate change in entropy in free expansion. Then

Srev= Sf-Si= fi Q/T= 1/Tf

iQ (isothermal)

An ideal gas confined in a insulated cylinder fitted with a piston . The cylinder rest on a thermal reservoir maintained at temp T.

Gas is expanded isothermally from I to f state and heat is absorbed by the gas from the reservoir.S is positive because Q is positive

S= Sf-Si= Q/T

Ch 20-3,4 Change in Entropy, Second Law of Thermodynamics

Entropy as a State functionS= Sf-Si= Q/T but

Eint=Q-W or Q = Eint+W ; W=pdV; Eint= nCVT

Then S= Q/T= if (nCVdT/T) +

if (pdV/T)

=nCV if (dT/T) +

if (nRdV/V)

S =nCV ln(Tf/Ti) + nR ln(Vf/Vi) Second Law of Thermodynamics In a closed system entropy remains constant for

reversible process but it increases for irreversible process.

Entropy never decreasesChange in Entropy of a reversible compression

of an ideal gas in a closed system reservoir + gas

Ssys= Sgas + Sres =-Q/T+Q/T=0

A Carnot engine is a device that extracts heat QH from a reservoir at temperature TH, does useful work W and rejects heat QL to a reservoir at temperature TL.

On a p-V diagram Carnot cycle ( executed by a cylinder fitted with a piston and in thermal contact with one of two reservoirs at temperatures TH and TL.) is bound by two isotherms and two adiabatic.

Ch 20-5 Entropy in Real World: Engines

Ch 20-5 Entropy in Real World: Engines

Heat QH is absorbed at Temperature TH and heat QL is rejected at TL.

Work: According to first law of thermodynamics, Eint=Q-W, Eint=0

and W=Q=QH-QL Entropy Change S:In Carnot cycle S=0S=0= QH/TH-QL/TL

QH/TH=QL/TL

Ch 20-5 Entropy in Real World: Engines

Thermal Efficiency of an Engine :

= work we get /energy we pay for = W/ QH

For a Carnot engine W=QH-QL

Then Carnot engine efficiency C is

C : QH-QL/QH

C=1-QL/QH=1- TL/TH

There is no perfect engine i.e. QL=0

Ch 20-6 Entropy in Real World: Refrigerators

A refrigerator is an engine that uses work to transfer heat from a

low-temperature reservoir to a high-temperature reservoir

as the engine repeats a set series of thermodynamic processes.

I

Refrigerators

) )

n the household refrigerator the work is provided by the

compressor and it transfers heat from the food storage area

low-temperature reservoir to the surrounding air

high-temperature reservoir . In an air conditioner

the low-temperature reservoir is the room that is being cooled.

The high-temperature reservoir is the outdoor air. An ideal

refrigerator is one in which all the processes are reversible

One such refrigerator is a Carnot engine that operates

in the reverse order:

This is known as a Carnot refrigerator.

and

no energy is lost to friction or turbulence.

a d c b a→ → → →

Ch 20-6 Entropy in Real World: Refrigerators

A Refrigerator: A device that uses work to transfer energy QL from a low temperature reservoir at temperature TL to a high-temperature reservoir at temperature TH

Coefficient of performance of a refrigerator K

K= what we want /what we pay for K=QL/W but W=QH-QL K =QL/W=QL/QH-QLK =QL/QH= TL/TH-1K=TL/(TH-TL)There is no perfect refrigerator i.e.

W=0

Suggested problems Chapter 20