Basic thermodynamics PPT

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27 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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1

Outline


Define terms and conventions


Introduce 1
st

law of thermodynamics


Contrast state and non
-
state properties


Describe the Carnot cycle


2

System and environment


System

= what we wish to study


View as
control mass
or
control volume


Control mass (CM)


Define some mass, hold fixed, follow it around


Control volume (CV)


Define and monitor a physical space


Environment

= everything else that may
interact with the system

3

System states


Systems may be
open

or
closed
to mass


Open systems permit mass exchange across system
boundaries


Our CVs are usually open


Strictly speaking, a CM is closed


Closed systems may be
isolated

or
nonisolated


Isolated systems do not permit energy transfer with
environment


Closed, isolated system = environment doesn’t matter

4

Lagrangian

vs.
Eulerian


CM is the
Lagrangian

viewpoint


Powerful, desirable but often impractical


Total derivatives


Freeway example


CV is the
Eulerian

viewpoint


Observe flow through volume


Partial derivatives

5

Air parcel


Our most frequently used system


CM (usually!)


Lagrangian

concept


Monitor how T, p, and V change as we follow
it around

6

Conventions


We often use CAPITAL letters for
extensive

quantities, and lower case for
specific

quantities


Specific = per unit mass


Example:


U is internal energy, in Joules


u is specific internal energy, in J/kg


Unfortunately, “u” is also zonal wind velocity


Exceptions:


Temperature T is essentially specific, but capitalized
(and isn’t per unit mass anyway)


Pressure p is fundamentally extensive, but lower case

7

Energy and the 1
st

law


Total energy = KE + PE + IE


Conserved in absence of sources and sinks


Our main use of 1
st

law: monitor changes in
internal energy (IE or u) owing to sources and
sinks


How do we change system u? With energy
transfer via


heat Q or q


w
ork W or w


Caveat: w is also vertical velocity, and q will be
reused (briefly) for water vapor specific humidity

8

Work


Work = force applied over a distance


Force: N, distance: m


Work: Nm = J = energy


Our principal interest: CM volume
compression or expansion (
dV
) in presence of
external pressure (p)




W > 0 if
dV

> 0

9

Work

10

W > 0 when system expands against

environment

Heat


Diabatic

heat


Diabatic: Greek for “passable, to be passed
through”


Internal energy exchanged between system and
environment


q > 0 when energy flow is INTO system


Adiabatic
= system is
isolated


Adiabatic
: impassable, not to be passed through

11

Caution on nomenclature


We should use
diabatic

when the energy exchange is
between system and environment


But, what if the heat source or sink is
inside

the system?


That’s adiabatic, but q ≠ 0


Our interior heat source will be water changing phase


Dry adiabatic
: q = 0


No heat source, outside OR inside


“dry” really means no water phase changes


Moist adiabatic
: q ≠ 0, but heat source/sink is
inside
system


“moist” implies water phase change


Synonyms include “saturated adiabatic” and “wet adiabatic”


Can also be referred to as “diabatic”!


12

1
st

law


In the absence of ∆KE and ∆PE




Other ways of writing this


13

Most of my examples will be per unit mass.

State properties


Internal energy u is a
state property


Changes in state properties are not path
-
dependent




Other state properties include m, T, p,
r
, V,
etc.

14

State properties

15

Path
-
dependence


Work and heat are
path
-
dependent

16

Path
-
dependence


A
cyclic

process starts
and ends with the same
state property values







… but the cyclic process
can have
net heat
exchange

and do
net
work

17

Path
-
dependence

18

Path
-
dependence

19

Carnot cycle


4
-
step piston cycle on a CM


2 steps of volume expansion, 2 of volume
compression


2 steps are isothermal, 2 are (dry) adiabatic


Warm and cold thermal reservoirs external to
system


Start and end with temperature T
1

and
volume V
1

20

Carnot


Step 1

21

Isothermal volume expansion


Add heat Q
A

from warm

reservoir


T
2

= T
1

V
2

> V
1




Carnot


Step 2

22

Adiabatic volume expansion


No heat exchange



T
3

< T
2

V
3

> V
2




Carnot


Step 3

23

Isothermal volume compression


Lose heat Q
B

to cold thermal

reservoir


T
4

=

T
3

V
4

<

V
3




Carnot


Step 4

24

Adiabatic volume compression


No heat exchange



T
1

> T
4

V
1

<

V
4




Returned to original state T
1
, V
1
.

Cycle is complete.

25

Apply 1
st

law





26

Carnot on T
-
V diagram

27

Carnot on T
-
V diagram

28

Carnot on T
-
V diagram

29

Carnot on T
-
V diagram

30

Carnot on T
-
V diagram

31

Carnot on T
-
V diagram

32

Carnot on T
-
V diagram

33

No net ∆V

But did net W

Conceptual summary

34

Heat flow diverted

t
o do work

Question for thought #1

35

The isothermal expansion (Q
A
) occurred at a

higher temperature than the

Isothermal compression (Q
B
).

What does this imply for the work?


Q
B

is waste heat.


What does this imply for the


efficiency of this heat engine?


Is there a limit to efficiency?

Is the limit found in the 1
st

law?

Question for thought #2

36

Can you design a cyclic process that does
no net work?


What would it look like on a T
-
V diagram?

Summary


1
st

law says, in essence, if you can’t take the
heat, you can’t do the work


Work and heat are path
-
dependent


Carnot cycle illustrates isothermal and (dry)
adiabatic processes


Heat diverted to do work, but some is wasted







W = Q
A

-

Q
B



37