Ideal Gas Summary

Ideal gas summary
* Assume no




R=¥fy¥ &
" " ["J / moth ]
Ideal
gas equation
: PU = RT -




temperature car ] interaction
pressure [ Nlm
'
-5Pa]\ specific volume Embry ] between
gas
(
molecular weight [ kglmol ] molecules
Ideal for
gas law pV=mRI
17¥
: a fixed mass : =



ET = * Ideal
gases
don't exist
mslmolpv =④ÑT * For dense like
number of moles
gases
water
vapor ,
use

equals ideal
compressibility factor :
,¥
Z 1 for tables
gas
=
, steam

- change in energy .




Internal
energy
of ideal
gas is a function
T2
of
temperature
specific heat
:
cult
/ )=d or do =
Cult)dT


Change in internal
energy : Ulta ) -
ULT, ) S cult )dT
=

capacity for constant volume [ KJ /
high ]
T
,
"""
"%
Enthalpy of ideal
gas is a function of temperature : Cpct)
)
=



If
or dh =
Cplt )dT
T2 heat " ""
specific 2


Change in
enthalpy :ht2 ) h (F) - =


T
fcplt)dT capacity for constant pressure Quasi static work :W= SPDÑ
(
, '
pressure

:h(T) UCT ) pit ULT ) RT
Enthalpy = + = t First law : ou
heat
= Q
1
interaction
-

w -

work
interaction




Cplt)=GCT)tR

}
Relation between Cp and Cu :
Cplt ) = KR
Equation of state !
pV=mRT
K -
1




Specific heat ratio : KLT) Cp ( T)
Rcr
cult )
=
=




) (T K -

l


if Cv and Cp are constant : ou =mGOT
OH
=mCpDT 2

Iso choric process (constant volume ) : dV=o → W=0 → Q =
ou = m
{ Cvdt ,
if Cv =
const → Q=mG( I F) [j ] -




2

Isobaric process (constant pressure ) :W=p(V2 -

V , )=mR( Tz -

T, ) ,
first law : Q -

POV = OU →
Q =oH=fmCpdT
if
Cp const Q Mcp ( Tz T ) [ J]
= → = -



z
.



,



Q=w=fpdV=mRTln) ,)
Isothermal process ( constant temp ) .
: OU = oh =
0 → =P ,V
,
In
T
heat interaction p=mRTÑ
2-
Adiabatic process (no heat ):dQ=0
"


¥- )
" "



1¥ -1¥)
interaction k=cpkv→
1¥
=
/ , , =




Work for adiabatic
process : W = -
ou =mCv(T ,
-


Tz ) Quasistatic poly Tropic process
: PV
"
= constant ,
I < nck

not :
W (P V P2 V2 ) special ± A
pro
quasi static
÷ cases isochoric : n =
const
-

: =
-
- •
,
.

, ,

,
isobaric const
pro
•
: n = 0 =




( (,P÷)^)
,




quasi static W
=ng¥T I isothermal h=1 Pv const
•
: -
: =
.

,



quasi static adiabatic
"
• :
h=K=Cpkv , PV =
const .




Work in
polyTropic
process
:




,T÷ -1¥ ) =/¥ )
" "
if n -41 W=mRlTz ti ) -


Ideal gas in
poly Tropic process :


l -
n



W=mR( Ta
W=mRTln(V÷ ) )
it n =L if h =/ I -
T
,

( isothermal ) 1 -
n
Heat interaction :
it
W=mRTln(¥ ) ¥1
Q=mCv(nn)(T2 )
n =L if n
-



Ti
( isothermal )
,




if h
( isothermal :0U=o
=L Q=W=mRT
) #-) In



?⃝