Thermodynamics- Entropy

Question 1

What is the Clausius inequality?

Answer 1

The cyclic integral of δQ/T is always less than or equal to 0.
Where δQ/T is the sum of all the differential amounts of heat transfer to or from the system divided by the temperature at the boundary of the system.

Question 2

What is the Clausius inequality for internally reversible cycles?

Answer 2

The cyclic integral of δQ/T is equal to 0

Question 3

What is the definition equation for entropy?

Answer 3

dS=(δQ/T)int,rev

Question 4

Is entropy an intensive or extensive property of a system?

Answer 4

Extensive so depends on mass. If entropy per unit mass, this is intensive.

Question 5

How to calculate entropy change of a system

Answer 5

S2-S1
Or integrate δQ/T between initial and final states
Doesn’t matter if the process is reversible or irreversible.

Question 6

What is the increase of entropy principle?

Answer 6

The entropy of an isolated system dunking a process always increases or, in the limiting case of a reversible process, remains constant.

Question 7

What effect do irreversibilities have on entropy?

Answer 7

They increase it

Question 8

Can a system have a negative entropy change?

Answer 8

Yes but the total entropy change for the system and its surroundings is always greater than or equal to 0. The system and its surroundings form an isolated system.

Question 9

What direction must a process proceed in?

Answer 9

The direction that complies with the increase of entropy principle.

Question 10

Is there a conservation of entropy principle?

Answer 10

No

Question 11

What does a greater extent of irreversibilities mean about entropy generation?

Answer 11

Entropy generation is greater. Therefore entropy generation can be used as a quantitative measure of irreversibilities associated with a process.

Question 12

What is the substance used with an entropy defined as zero?

Answer 12

Saturated liquid water at 0.01°C. Lower temperature will have negative entropy.

Question 13

How to calculate entropy in the saturated liquid-vapour region

Answer 13

Need quality of mixture.
S=Sf+xSfg (really S is s)
Values of Sf and Sfg determined from the saturation tables
Sfg is Sg-Sf

Question 14

Approximate formula for compressed liquid entropy

Answer 14

S@T,P=Sf@T

Where Sf@T is from the saturation tables

Question 15

Graph of temperature against entropy for a pure substance

Answer 15

The saturated line is like a bell curve with a peak at the critical state. The constant pressure lines are parallel to x-axis under curve and form ‘upstairs’ shape and almost follow saturated liquid line. Constant specific volume lines steeper than constant pressure lines and are never horizontal (under saturated curve they are curve with decreasing gradient, after saturated vapour line they are diagonal).

Question 16

What is an isentropic process?

Answer 16

One during which the entropy remains constant.

Question 17

Example characteristics of an isentropic process

Answer 17

It is adiabatic and internally reversible.

Question 18

When can a process be isentropic but not adiabatic or internally reversible?

Answer 18

The entropy increase of a substance during the process due to irreversibilities may be offset by a decrease in entropy due to heat losses.

Question 19

What does the area under a T against S curve for an internally reversible process represent?

Answer 19

The total heat transfer during the process. Also works for per unit mass.

Question 20

Relationship between temperature and entropy for internally reversible isothermal process

Answer 20

Qint,rev = T0ΔS
T0 is is the constant temperature
Makes the integration calculation for heat transfer easy

Question 21

Graph of temperature against entropy for isentropic process

Answer 21

Vertical line segment. Because isentropic process involves no heat transfer so area under its process path must be 0

Question 22

Enthalpy against entropy diagram for steady-flow devices

Answer 22

Has two points to represent inlet and exit states and the process path between them. The vertical distance between points is Δh (measure of work output of turbine) and the horizontal distance is Δs (measure of the irreversibilities associated with the process.

Question 23

Temperature against entropy diagram for Carnot cycle

Answer 23

Forms a rectangle. Starts at (S1,TH) then (S2,TH). Then goes down to (S2,TL) then left to (S1,TL) then back to start. The net work is the area enclosed. The area under top edge is QH and the area under bottom edge is QL.

Question 24

Derive the Gibbs equation

Answer 24

Start with δQint rev - δWint rev,out = dU
But the δQ=TdS and δW=PdV
So TdS=dU+PdV
V is volume
Works for all systems

Question 25

Derive the 2nd Tds equation (still a Gibbs relation)

Answer 25

``` Eliminates dU Start with Gibbs equation and H=U+PV dH=dU+PdV+VdP So TdS=dU+PdV goes to TdS=dH-VdP V is volume Works for all systems ```

Question 26

Finding entropy change of liquids and solids (incompressible substances)

Answer 26

Use Gibbs equation but dV is 0 so ds=du/T du is cdT so ds=cdT/T Integrate between the inlet and exit states Get Δs=c(avg)ln(T2/T1)

Question 27

Finding entropy change of ideal gases using specific volumes

Answer 27

Start with Gibbs equation but du=cvdT and P=RT/v So ds = cvdT/T + Rdv/v Integrate from exit to inlet states to get Δs This is used for a process with no flow Can use cv(avg) to simplify

Question 28

Finding entropy change of ideal gases using pressures

Answer 28

Start with 2nd Tds equation but dh=cpdT and v=RT/P So ds = cpdT/T - Rln(P2/P1) Integrate between exit and inlet states to get Δs This is used for steady-flow processes. Can use cp(avg) to simplify

Question 29

Finding reversible work output of internally reversible process in a steady-flow device using fluid properties

Answer 29

Start with overall energy balance δqrev-δwrev=dh+dke+dpe But δqrev is Tds and Tds is dh-vdP So -δwrev = vdP + dke +dpe Integrate to get wrev = -integral of vdP -Δke -Δpe ke and le changes often negligible so wrev= -integral of vdP from exit to initial states Gives negative results when work is done on the system

Question 30

What is the isentropic efficiency of a turbine?

Answer 30

Ratio of actual work output of the turbine to the work output that would be achieved if the process between the inlet state and exit pressure was isentropic. Equal to (h1-h2a)/(h1-h2s) Numbers correspond to initial and final states a means actual, s means isentropic.

Question 31

Enthalpy against entropy diagram for calculating isentropic efficiency of turbines

Answer 31

Has diagonal line for P1 above and steeper than that for P2. Isentropic process has process path line as vertically down from inlet state on P1 line to exit state on P2 line. Actual process has process path line from same inlet state on P1 but goes further right until it reaches P2 line due to an increase in entropy. h1 is same for both. h2a is higher than h2s so ws is greater than wa.

Question 32

What is the isentropic efficiency of a compressor?

Answer 32

``` The ratio of the work input required to raise the pressure of a gas to a specified value in an isentropic manner to the actual work input. Equal to (h2s-h1)/(h2a-h1) when ke and pe change negligible ```

Question 33

What is the isentropic efficiency of a pump?

Answer 33

Similar to compressor but can also be represented by | v(P2-P1)/(h2a-h1)

Question 34

Enthalpy against entropy diagram for calculating isentropic efficiency of compressors

Answer 34

Same as one for turbines but the initial state is on the the lower pressure line (redefined as P1 line). Means h2a is higher than h2s so the work input required is greater for the actual process.

Question 35

Isothermal efficiency of a compressor

Answer 35

wt/wa Where wt is required work input for reversible isothermal process And wa is required work input for actual process Used when compressor is not designed to be adiabatic but at a constant temperature where it is intentionally cooled.

Question 36

Increase in entropy principle equation

Answer 36

Sin-Sout+Sgen=ΔSsystem

Question 37

Entropy transfer by heat transfer equations

Answer 37

Entropy transfer = Q/T for T constant | Or is integral of δQ/T between initial and final states

Question 38

Can entropy be transferred by work?

Answer 38

No

Question 39

What can you say about entropy transfer when two systems are in contact?

Answer 39

The entropy transfer form the warmer system is equal to the entropy transfer into the cooler one at the point of contact

Question 40

Entropy transfer by mass equation

Answer 40

Smass=ms

Question 41

Is any entropy generated during a reversible process?

Answer 41

No

Question 42

When evaluating entropy transfer between a system and its surroundings, what is the boundary temperature?

Answer 42

The environment temperature