Lecture 9 - Reversible Work Flashcards
What is the equation for work of a closed system?
Wb = PdV
Use the first law to write an expression for reversible steady work (in an open system).
Assuming no heat transfer or change in kinetic or potential energy:
Q̇ - Ẇ = ṁ[h2-h1 + (V2^2 - V1^2)/2 + g(z2-z1)]
-Ẇ = ṁ[h2-h1]
Dividing by the mass-flow rate:
-w = h2-h1 [in kJ/kg]
Use the first law to write an equation for work in a steady flow device undergoing a reversible process.
δq(rev) - δw(rev) = dh + dke + dpe
with entropy, δq(rev) = Tds
from Gibb’s second equation, Tds = dh - vdP
Combining the two equations we get:
δq(rev) = dh - vdP
SUBSTITUTING THE ABOVE INTO THE FIRST LAW,
dh - vdP - δw(rev) = dh + dke + dpe
WE NOW HAVE THE FOLLOWING:
- δw(rev) = vdP + dke + dpe
INTEGRATING between two states WE GET:
-wrev = v(P2P1) + Δke + Δpe [kJ/kg]
IGNORING KINETIC AND POTENTIAL ENERGY:
wrev = -v(P2P1)
Give the expression for work in an open reversible system.
wrev = -v(P2P1)
Give the expression for boundary work in a closed system.
Wb = 1∫2 Pdv
In pumps and compressors, we do work …
on the system, which means we do negative work
Write the expression for work in a pump or compressor.
w(rev) = -[-v(P2-P1)] = 1∫2 vdP
The amount of work done in a compressor depends on …
the type of process
In compression, we move from …
a lower pressure, P1 to a higher pressure, P2
Isentropic processes are those that …
are both adiabatic and reversible
In an isentropic (adiabatic and reversible) compression process, we relate pressure and volume by the relation …
Pv^k = cte
In isothermal compression, we relate pressure and volume by the expression …
Pv = cte
Real compression processes are …
polytropic
A polytropic process is …
somewhere between isentropic and isothermal
In a polytropic process, we relate pressure and volume by the equation …
Pv^n = cte
where n = some power between 1
In a polytropic process, we relate pressure and volume by the equation …
Pv^n = cte
where n = some power between 1 and k (1
W(rev)in = +1∫2 vdP. Draw this on a P-v diagram. What does W(rev)in = +1∫2 vdP represent on the diagram?
P
2
dP =========\
│ 1
v (represents the specific volume; an
actual volume value!)
W(rev)in = +1∫2 vdP represents the area to the left of the P-v curve of an isentropic, polytropic, or isothermal process
_____________ process has the least amount of work, and ___________ has the most work.
Isothermal
Isentropic
Heat exchangers (el termocambiador/ intercambiador de calor) _______ gases
cool
When you cool a gas, the specific volume __________.
decreases
Density, ρ, =
ρ = P/(RT)
Specific volume, v, =
v = 1/ρ = RT/P
Intercoolers reduce the temperature of the gas.
True
Intercoolers are …
gas to liquid or gas to air heat exchangers
reversible means ….
no friction, viscous dissipation, rapid expansion, or heat transfer across finite temperatures
Write the first law for a static, adiabatic open system.
- Ẇ = ṁ[h2-h1]
Write the first law for a static, adiabatic turbine.
Ẇ = -ṁ[h2-h1] bcz for a turbine, work is positive
What is the adiabatic efficiency of a turbine?
η(Turbine) = Actual work/Isentropic work
where the mass flow rate cancels because it is the same for both turbines
actual work = -ha+h1 (on mollier diagram for the real entropy)
isentropic work = -h2+h1 on the Mollier diagram
What is the Mollier Diagram?
A plot of enthalpy vs entropy where we go from high pressure to low pressure in an expansion device
In reality, when we go through a turbine, we have irreversibilities, and the entropies increase.
True
In isentropic expansion, we can say that the entropy …
remains the same; s1 = s2
Work in a compressor is positive or negative?
negative because work is done on the system
What is the equation for work in a compressor?
w = h2-h1
What is the first law for a static adiabatic compressor?
-Ẇ = ṁ[h2 - h1]
What is the efficiency of a compressor?
η = Isentropic Work/Actual Work
where isentropic work = h2s - h1 (on the mollier diagram)
actual work = h2a-h1 on the mollier diagram
When dealing with an incompressible fluid, W(rev) =
W(rev) = 1∫2 vdP W(rev) = v(P2-P1)
The efficiency of a pump, ηP, =
ηP = Isentropic work/Isentropic work ηP = v(P2-P1)/(h2a-h1)
What is a nozzle (boquilla/tobera)?
a device that accelerates a flow by converting high pressure in a static fluid into kinetic energy
What is the first law with respect to a nozzle and why?
- Δh = ΔKE
- h2+h1 = V2^2/2
because there is no heat transfer, so it is adiabatic, and all of the energy is kinetic, so we can drop the potential energy
Also, a nozzle does not do work, so we drop Ẇ, and ṁ.
WE ALSO ASSUME THAT VELOCITY ON THE INLET ~ = 0 & VELOCITY AT THE EXIT IS NOT 0.
Does a nozzle do work?
NO
What is the isentropic efficiency of a nozzle?
ηN = Actual kinetic energy @ exit/Isentropic kinetic energy @ exit
ηN = V2actual^2/V2isentropic^2 = -h2a+h1/ -h2s+h1
-h2a+h1 = V2actual^2/2 & -h2s+h1 = V2isen^2/2 only works when …
V1 ~= 0
In a nozzle, we go from high entropy to low entropy.
True
we also go from high pressure to low pressure
State the entropy generation equation.
Ṡgen = Σṁoutsout - Σṁinsin - ΣQ̇k/Tk
We treat air like an ideal gas.
True
We account for changing specific heats in a process by using …
s2^0 - s1^0
A watt is the unit of measurement for power. What is the conversion in joules per second?
1 Watt = 1 J/s
1MPa = ? bar
1MPa = 10 bar
Power in Spanish.
Poder
energía
Potencia
