Lecture 9 - Reversible Work

Question 1

What is the equation for work of a closed system?

Answer 1

Wb = PdV

Question 2

Use the first law to write an expression for reversible steady work (in an open system).

Answer 2

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]

Question 3

Use the first law to write an equation for work in a steady flow device undergoing a reversible process.

Answer 3

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)

Question 4

Give the expression for work in an open reversible system.

Answer 4

wrev = -v(P2P1)

Question 5

Give the expression for boundary work in a closed system.

Answer 5

Wb = 1∫2 Pdv

Question 6

In pumps and compressors, we do work …

Answer 6

on the system, which means we do negative work

Question 7

Write the expression for work in a pump or compressor.

Answer 7

w(rev) = -[-v(P2-P1)] = 1∫2 vdP

Question 8

The amount of work done in a compressor depends on …

Answer 8

the type of process

Question 9

In compression, we move from …

Answer 9

a lower pressure, P1 to a higher pressure, P2

Question 10

Isentropic processes are those that …

Answer 10

are both adiabatic and reversible

Question 11

In an isentropic (adiabatic and reversible) compression process, we relate pressure and volume by the relation …

Answer 11

Pv^k = cte

Question 12

In isothermal compression, we relate pressure and volume by the expression …

Answer 12

Pv = cte

Question 13

Real compression processes are …

Answer 13

polytropic

Question 14

A polytropic process is …

Answer 14

somewhere between isentropic and isothermal

Question 15

In a polytropic process, we relate pressure and volume by the equation …

Answer 15

Pv^n = cte

where n = some power between 1

Question 16

In a polytropic process, we relate pressure and volume by the equation …

Answer 16

Pv^n = cte

where n = some power between 1 and k (1

Question 17

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?

Answer 17

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

Question 18

_____________ process has the least amount of work, and ___________ has the most work.

Answer 18

Isothermal

Isentropic

Question 19

Heat exchangers (el termocambiador/ intercambiador de calor) _______ gases

Answer 19

cool

Question 20

When you cool a gas, the specific volume __________.

Answer 20

decreases

Question 21

Density, ρ, =

Answer 21

ρ = P/(RT)

Question 22

Specific volume, v, =

Answer 22

v = 1/ρ = RT/P

Question 23

Intercoolers reduce the temperature of the gas.

Answer 23

True

Question 24

Intercoolers are …

Answer 24

gas to liquid or gas to air heat exchangers

Question 25

reversible means ....

Answer 25

no friction, viscous dissipation, rapid expansion, or heat transfer across finite temperatures

Question 26

Write the first law for a static, adiabatic open system.

Answer 26

- Ẇ = ṁ[h2-h1]

Question 27

Write the first law for a static, adiabatic turbine.

Answer 27

Ẇ = -ṁ[h2-h1] bcz for a turbine, work is positive

Question 28

What is the adiabatic efficiency of a turbine?

Answer 28

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

Question 29

What is the Mollier Diagram?

Answer 29

A plot of enthalpy vs entropy where we go from high pressure to low pressure in an expansion device

Question 30

In reality, when we go through a turbine, we have irreversibilities, and the entropies increase.

Answer 30

True

Question 31

In isentropic expansion, we can say that the entropy ...

Answer 31

remains the same; s1 = s2

Question 32

Work in a compressor is positive or negative?

Answer 32

negative because work is done on the system

Question 33

What is the equation for work in a compressor?

Answer 33

w = h2-h1

Question 34

What is the first law for a static adiabatic compressor?

Answer 34

-Ẇ = ṁ[h2 - h1]

Question 35

What is the efficiency of a compressor?

Answer 35

η = Isentropic Work/Actual Work where isentropic work = h2s - h1 (on the mollier diagram) actual work = h2a-h1 on the mollier diagram

Question 36

When dealing with an incompressible fluid, W(rev) =

Answer 36

``` W(rev) = 1∫2 vdP W(rev) = v(P2-P1) ```

Question 37

The efficiency of a pump, ηP, =

Answer 37

``` ηP = Isentropic work/Isentropic work ηP = v(P2-P1)/(h2a-h1) ```

Question 38

What is a nozzle (boquilla/tobera)?

Answer 38

a device that accelerates a flow by converting high pressure in a static fluid into kinetic energy

Question 39

What is the first law with respect to a nozzle and why?

Answer 39

- 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.

Question 40

Does a nozzle do work?

Answer 40

NO

Question 41

What is the isentropic efficiency of a nozzle?

Answer 41

ηN = Actual kinetic energy @ exit/Isentropic kinetic energy @ exit ηN = V2actual^2/V2isentropic^2 = -h2a+h1/ -h2s+h1

Question 42

-h2a+h1 = V2actual^2/2 & -h2s+h1 = V2isen^2/2 only works when ...

Answer 42

V1 ~= 0

Question 43

In a nozzle, we go from high entropy to low entropy.

Answer 43

True we also go from high pressure to low pressure

Question 44

State the entropy generation equation.

Answer 44

Ṡgen = Σṁout*sout - Σṁin*sin - ΣQ̇k/Tk

Question 45

We treat air like an ideal gas.

Answer 45

True

Question 46

We account for changing specific heats in a process by using ...

Answer 46

s2^0 - s1^0

Question 47

A watt is the unit of measurement for power. What is the conversion in joules per second?

Answer 47

1 Watt = 1 J/s

Question 48

1MPa = ? bar

Answer 48

1MPa = 10 bar

Question 49

Power in Spanish.

Answer 49

Poder energía Potencia