Thermodynamics- Entropy Flashcards
What is the Clausius inequality?
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.
What is the Clausius inequality for internally reversible cycles?
The cyclic integral of δQ/T is equal to 0
What is the definition equation for entropy?
dS=(δQ/T)int,rev
Is entropy an intensive or extensive property of a system?
Extensive so depends on mass. If entropy per unit mass, this is intensive.
How to calculate entropy change of a system
S2-S1
Or integrate δQ/T between initial and final states
Doesn’t matter if the process is reversible or irreversible.
What is the increase of entropy principle?
The entropy of an isolated system dunking a process always increases or, in the limiting case of a reversible process, remains constant.
What effect do irreversibilities have on entropy?
They increase it
Can a system have a negative entropy change?
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.
What direction must a process proceed in?
The direction that complies with the increase of entropy principle.
Is there a conservation of entropy principle?
No
What does a greater extent of irreversibilities mean about entropy generation?
Entropy generation is greater. Therefore entropy generation can be used as a quantitative measure of irreversibilities associated with a process.
What is the substance used with an entropy defined as zero?
Saturated liquid water at 0.01°C. Lower temperature will have negative entropy.
How to calculate entropy in the saturated liquid-vapour region
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
Approximate formula for compressed liquid entropy
S@T,P=Sf@T
Where Sf@T is from the saturation tables
Graph of temperature against entropy for a pure substance
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).
What is an isentropic process?
One during which the entropy remains constant.
Example characteristics of an isentropic process
It is adiabatic and internally reversible.
When can a process be isentropic but not adiabatic or internally reversible?
The entropy increase of a substance during the process due to irreversibilities may be offset by a decrease in entropy due to heat losses.
What does the area under a T against S curve for an internally reversible process represent?
The total heat transfer during the process. Also works for per unit mass.
Relationship between temperature and entropy for internally reversible isothermal process
Qint,rev = T0ΔS
T0 is is the constant temperature
Makes the integration calculation for heat transfer easy
Graph of temperature against entropy for isentropic process
Vertical line segment. Because isentropic process involves no heat transfer so area under its process path must be 0
Enthalpy against entropy diagram for steady-flow devices
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.
Temperature against entropy diagram for Carnot cycle
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.
Derive the Gibbs equation
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
Derive the 2nd Tds equation (still a Gibbs relation)
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
Finding entropy change of liquids and solids (incompressible substances)
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)
Finding entropy change of ideal gases using specific volumes
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
Finding entropy change of ideal gases using pressures
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
Finding reversible work output of internally reversible process in a steady-flow device using fluid properties
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
What is the isentropic efficiency of a turbine?
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.
Enthalpy against entropy diagram for calculating isentropic efficiency of turbines
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.
What is the isentropic efficiency of a compressor?
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
What is the isentropic efficiency of a pump?
Similar to compressor but can also be represented by
v(P2-P1)/(h2a-h1)
Enthalpy against entropy diagram for calculating isentropic efficiency of compressors
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.
Isothermal efficiency of a compressor
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.
Increase in entropy principle equation
Sin-Sout+Sgen=ΔSsystem
Entropy transfer by heat transfer equations
Entropy transfer = Q/T for T constant
Or is integral of δQ/T between initial and final states
Can entropy be transferred by work?
No
What can you say about entropy transfer when two systems are in contact?
The entropy transfer form the warmer system is equal to the entropy transfer into the cooler one at the point of contact
Entropy transfer by mass equation
Smass=ms
Is any entropy generated during a reversible process?
No
When evaluating entropy transfer between a system and its surroundings, what is the boundary temperature?
The environment temperature
