2 - thermodynamics

8/3/2019 2 - Thermodynamics

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Thermodynamics

1



• To tell us the relationshi between the ressure, tem erature and

density of a gas as it moves.

• Altogether there are 6 variables we need to describe the state of a

gas…• p pressure (Pa)

• density (kg/m3), or specific volume v =1/

• T temperature (K)

• h enthalpy ( ), he+ p/

• s entropy ( )

•

1. The Kinetic Theory of Gases,

2. The 1st Law of Thermodynamics, 3. S eci ic Heats

4. The 2nd Law of Thermodynamics

2



.

•

• Gas is

a collection

of

molecules

in

random

motion

• Molecules bounce of each other like hard spheres

• Gives two sets of relations… Neglects forces

between molecules

Gas constant

R = 287 J/kg/K

for air

• Gases that obey these relations are called “Thermally

3Perfect”



•

class, but

this

isn’t

always

true…

Ceases

to

be

valid

.

Why?

4



st.

“Energy is Conserved”W

E QChange in

Amount of work

W Q E

Collection of identified

gas molecules

(System)

energymoun o

heat addedone y pressure

and viscous forces

Work =

p V (<0)

Surface area S

5



…

pdvdedq

6



.

• Specific heat – amount of heat needed to raise the

temperature of 1kg by 1 Kelvin

• Two kinds: T

q

T

q

C

• Specific heat at constant volume

• Specific heat at constant pressure

vv q

p p

T qC ) / (

7Pratt and

Whitney

JT58

Test

(Powered

SR71)



vdpdhdq pdvdedq

…

8



dT

dhC p

dT

deC v

•

A gas that is thermally perfect and for which the…

… , …

• We will assume calorically perfect gases in this class, but…

9



nd. Shock in a Converging Diverging Nozzle

10Bourgoing &

Benay

(2005),

ONERA,

France Schlieren

visualization

Sensitive to in‐plane index of ref. gradient



• ‐ .

• Reversible Process

– no

dissipative

phenomena

occur.

• –

•nd –

Constant entropy.

Entropy – measure of disorder in the gas molecules.

increase entropy, but adding or removing heat may

increase or decrease entropy by an amount Q/T

• So…

11



…

dqTds For a reversible process…

pdvdedq 1st Law

e v

v RT p /

T erma y

perfect

gas

12



v p C C R v p C C /

…

13



1

1212

T ss

21 T C

e

v

2 – 1 …

14



SummaryAll gases Thermally perfect

perfect

)(T ee

• 1st Law pdvdedq )(T hh

•

Specific

dT deC v / vv

T eC ) / ( T C e v

• 2nd Law

p p p p

1

1212 log

T sse

• 2nd Law

21v

1

1

22 T 1

22

T p

15

11 T 11 T p

2 - thermodynamics

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