of Irreversibility
Increase Entropy Principle
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 1 Irreversibility and the Increase of Entropy Principle
Overview
Irreversibility Increase of entropy principle
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 2 Irreversibility and the Increase of Entropy Principle
Reversible and irreversible processes
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 3 Irreversibility and the Increase of Entropy Principle
A process for a closed system
Surroundings
Q
System
The heat transfer can place either reversibly or irreversibly.
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 4 Irreversibility and the Increase of Entropy Principle
The equivalent reversible process
T
Irreversible
2
T
2
1 S
For the system, replace the irreversible process by an equivalent reversible process, i.e., states A and B are the same.
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
1
Equivalent Reversible Process
S
Module 30 Slide 5 Irreversibility and the Increase of Entropy Principle
Reversible heat transfer at T1
Reservoir T1
dSreservoir,1 = -
Q1
Q rev,1 T1
System
dSsystem =
Q rev,1 T1
A series of reservoirs is used to transfer a finite amount of heat reversibly and bring the system to state 2.
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 6 Irreversibility and the Increase of Entropy Principle
Analysis of the process 1-2 and the First Law
Reversible Path, 1 - 2 U
2 1
U1-2 = Q1-2 - Wby,1-2 U 2 - U1 = Q1- 2 > 0 U 2 > U1
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 7 Irreversibility and the Increase of Entropy Principle
S
To return the system to the original state
Reversible Return Path, 2 - 1
U
2
1
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 8 Irreversibility and the Increase of Entropy Principle
S
To return the system to its original state via a reversible heat transfer
Reservoir 2 T2
dSreservoir, 2 = +
dSsystem = -
Q rev,1 T2
T2
Q1
System
Q rev,1
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 9 Irreversibility and the Increase of Entropy Principle
Analysis of the combined processes
1-2 2-1 Sum
Q W S U2-U1 +dQ1 0 S2-S U U1-U2 -dQ2 0 0 0 0 0
1
S1-S2
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 10 Irreversibility and the Increase of Entropy Principle
Examples of irreversible processes involving heat and work
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 11 Irreversibility and the Increase of Entropy Principle
Example 1 - Work input without heat transfer
Thermally Insulated, Q = 0 System Work Input, Win
U2 - U1 = Win
Here, work is converted into internal energy via an internally irreversible conversion of work into heat.
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 12 Irreversibility and the Increase of Entropy Principle
Example 1
General feature of the process when the system goes from T1 to T2 at constant pressure.
No heat transfer to the surroundings. Thus, entropy change of surroundings is zero. All of the entropy change is in the system. The is a temperature increase in the system.
Replace irreversible process with reversible process that accomplishes the same temperature change.
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 13 Irreversibility and the Increase of Entropy Principle
Example 1
Calculation of the entropy change
Assume a simple chemical system Let reversible process be isobaric with a work input, WI, to the system. Initial state: Ti, P Final state: Tf, P The conceptualization of the process is that work transfer takes place reversibly via a system of reservoirs over the temperature range.
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 14 Irreversibility and the Increase of Entropy Principle
Example 1
The entropy change of the system will be Tf Q R Sf - Si = Ti T
For the isobaric process, invoke the T-dS equation in the enthalpy form
TdS = dH - VdP
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 15 Irreversibility and the Increase of Entropy Principle
Example 1
TdS = dH - Vdp = C p dT dS = C p dT T
1- 2
S2 - S1 =
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
dT Cp T
Module 30 Slide 16 Irreversibility and the Increase of Entropy Principle
Example 1
For constant specific heat
Tf Sf - Si = CP ln T i Sf - Si > 0
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Because Tf > Ti, the entropy change of the universe is a positive quantity.
Module 30 Slide 17 Irreversibility and the Increase of Entropy Principle
Example 2: Dissipation of electrical energy into heat
Re
i
Q
Adiabatic Boundary
Q = U2 -U1
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Ssys > 0
Module 30 Slide 18 Irreversibility and the Increase of Entropy Principle
Example 2
net The result is the transformation of work into internal energy of a reservoir or system, and
Ssystem + Ssurroundin gs = Suniverse > 0
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 19 Irreversibility and the Increase of Entropy Principle
Example 3: Free expansion of an ideal gas
An ideal gas expands freely into a low pressure environment. Replacement process: Constant temperature expansion from initial to final state
Initial State: T, Vi Final State: T, Vf The entropy change of surroundings is zero. Ideal gas: PV = RT
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 20 Irreversibility and the Increase of Entropy Principle
Example 3
The entropy change is calculated from
QR = pdV
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
TdS = dU + pdV = pdV p dS = dV T
Module 30 Slide 21 Irreversibility and the Increase of Entropy Principle
Example 3
Sf - Si =
V
Vf
i
RdV V
Vf = R ln V i Sf - Si > 0
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 22 Irreversibility and the Increase of Entropy Principle
Example 4: External irreversibility via heat transfer at steady state
Reservoir 1
Q
T1 T2 T1
Q
System
Q
System
T2
Reservoir 2
Surroundings
Q
Q
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 23 Irreversibility and the Increase of Entropy Principle
Example 4
Reservoir 1
Q = U + Wby
Sreservoir,1 = - Q Ssystem = 0
Q
T1
System
Q
T1
T2
Reservoir 2
Sreservoir, 2 = + Q
T2
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 24 Irreversibility and the Increase of Entropy Principle
Example 4
Ssystem + Ssurroundings = Suniverse Q Q 0 + - + = Suniverse T1 T2 1 1 T -T Suniverse = Q - = Q 1 2 > 0 T T TT 1 2 1 2
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 25 Irreversibility and the Increase of Entropy Principle
Irreversibility
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki
Module 30 Slide 26 Irreversibility and the Increase of Entropy Principle
Type of irreversibility
External mechanical irreversibility Internal mechanical irreversibility External thermal irreversibility Chemical irreversibility
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 27 Irreversibility and the Increase of Entropy Principle
External mechanical irreversibility
Adiabatic dissipation of work into internal energy of a system. Associated with isothermal work transfers in contact with a reservoir
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 28 Irreversibility and the Increase of Entropy Principle
Adiabatic dissipation of work into heat
Water M Adiabatic The Joule Experiment
Heat, Work and Energy. A First Course in Thermodynamics 2009, F. A. Kulacki Module 30 Slide 29 Irreversibility and the Increase of Entropy Principle
The falling weight stirs the water. The external work transferred heats the water via friction; the heat is retained as an increas...