Irreversibility

Physics 313Professor Lee CarknerLecture 16

Exercise #15 Carnot EnginePower of engineh = 1 QH/QL h = W/QH Source temph = 1 TL/TH Max refrigerator COPFor a Carnot refrigerator operating between the same temperatures: Since K < KC (8.2

EntropyEntropy (S) defined by heat and temperature Total entropy around a closed reversible path is zero

Can write heat in terms of entropy:dQ = T dS

General Irreversibility

Since DS = Sf - SiSf > SiThis is true only for the sum of all entropies

Since only irreversible processes are possible,Entropy always increases

Reversible ProcessesConsider a heat exchange between a system and reservoir at temperature T So:dSs = +dQ/TdSr = - dQ/T For a reversible process the total entropy change of the universe is zero

Irreversible ProcessesHow do you compute the entropy change for an irreversible process?

What is the change in entropy for specific irreversible processes?

Isothermal W to UFriction or stirring of a system in contact with a heat reservoir

The only change of entropy is heat Q (=W) absorbed by the reservoir

DS = W/T

Adiabatic W to UFriction or stirring of insulated substance

System will increase in temperature

DS = dQ/T = CPdT/T = CPln (Tf/Ti)

Heat TransferTransferring heat from high to low T reservoir

For any heat reservoir DS = Q/T DS for cool reservoir = + Q/TC Assumes no other changes in any other system

Free ExpansionGas released into a vacuum Replace with a reversible isothermal expansion Thus, (dQ/T) = (nRdV/V) Note: Entropy increases even though temperature does not change

Entropy Change of SolidsSolids (and most liquids) are incompressible We can thus write dQ as CdT and dS as (C/T)dTIf we approximate C as being constant with T Note:

If C is not constant with T, need to know (and be able to integrate) C(T)

General Entropy ChangesFor fluids that under go a change in T, P or V we can find the entropy change of the system by finding dQ For example ideal gas:dQ = CPdT VdP dQ = CVdT + PdV These hold true for any continuous process involving an ideal gas with constant C

Notes on EntropyProcesses can only occur such that S increases Entropy is not conserved

The degree of entropy increase indicates the degree of departure from the reversible state

Use of EntropyHow can the second law be used?

Example: total entropy for a refrigerator DS (reservoir) = (Q + W) /THThe sum of all the entropy changes must be greater than zero:

Use of Entropy (cont.)We can now find an expression for the work: Thus the smallest value for the work is: Thus for any substance we can look up S1-S2 for a given Q and find out the minimum amount of work needed to cool it