Ideal Gas Laws Cheat Sheet

Phase-city matter homogenous chemicalphysical I
fied properties missing "Ideal gas find change
given
T u
: P V
Table
in

enthoh <po
uniforminvariable chemical composition
, ,
A-20 =

Pure subt -



P u :
T& cal X V
given
.

mc , Ur
KE/kg K
,

cpeT &Tz-avgCpY
, ,
:



Can exist phases but chemical remains tall
phases
.
in multiple same
2 Sh argcp (st) 155/1g
=
AV = 0 &
=
W = 0
rigid Vessel
=

Simple Compressible Sytm-commonly pure
subt.can be described

by intensive propt, VF =
VLig
for heat need Cak Mi far X
Table A-23 molar based

Vg =
Vap
↳ Q
use
specific valey for u
Cp@T, T2 h =
/Imol
State Principle
=
su
sh sh[molar]
for any Lindp intensive propt def values
Values K5/kmal- Sh
-

=
> =



(T V) G(P V) NOT (T P) -Particularly as
. .
,


,

of all other intensive propt .
, , ,
Cal
eng .

transferred by w & Q
for cylmde ulpiston


Hi ·nade
(x) for 2ph Lig-vap
Qualitytotal
: mix
,
ratio
of mass
of vapor present to v, m
,
P , if 5
cycledeal gas find W&Q each
proce
mixture mass
of Isobaric Q =
1 u + w
.




O-sat Lig
I- sat
use A-22(3) for u. 242
Meigt Muap
vap
lbfift [I] [R
&




Adiabatic Q = G

VL 14
=
Property
=
W
chart
-




Use Mc
transferred KI
=
wall
=f
m
·



V
= w . =



Total Val : Vi =
Meg +
Mrap
64 ·

Q = Xu + w
Isocaric W = 0

Q
My Mcig + Mrap AU
= =




Specific Val :
VT
Vigap 2 phase Vf
=
< V>
is Vg
Vig Vap Vspf find specific volume MYng
-




Vig (Mg Vi Eg sat
= :
+ mass
V = =
V
,
-




Unig
:


Arap X
vsat-usat-v (l-xf *g Ug -
=

X= Map = X Mtot = =
:




V (1 x) Vig Wrap (Mrap) (Urap my .




+
XVap
= - =




I
Mass-based vapor
fraction : Closed
System Energy Balance : same
for terms u, his

X Ma
e
& D-X) =Oned
Ske + SPE + 34 = Q -

w
bl based mass
function
Specific
(n2 u1)
k -
heat how much heat asarbs/releases
-
W = m -




:
subst
engwhen .




Internal
energy
:
ux
=
(1-X)ucig +
XUrap per unit temp change const Por v

Cp
R) for
> Cv
k =
<P/v
Enthalpy : he =
(l-x)hcg xhrap + ideal
gas
air
Cp-Cv =




15451bfft/maRCabm]
Ideal Gas
R 8 3145/malk com/mai
=



PV RT
.


Polytropic :
pun-const
n = 1 isothermal n = 0 Isobaric
Keyeg
=

TP const
Imd
Isovolum
#
.

= n = C
TRI
F [
=


PV nRT =
p :
#)5 PV MRT
=
Sub
forR TV = const -
> =




specific internal eng depends only Temp u(T) Cp (E)R canstp
rigid tank
·
on u = =




specific enthalpy depends only on
Temp h u(t) + =
RT Cv = (EYR constr
j Pc
total mass const
.




=> m , = mz = m

functionsof Talea -
.


heats both cap
specific Sh Cpst
-




↳..
specific vol
=

=> .
const Vi Vz= = v ⑯

du =
cu(T)dT u(Tz) n(T ) -
= cv(tz 5) - G
Vank
C
.
=
maT m
c p(T)dT h(tz) h(t) < p(tz 5) Utank = V =
m > =
-



dh =
-
= -


2
Vrank
tables to evaluate
changes in
specific internal
eng .
&
enthalpy = Mr =

V
=
Kg total mass


justified where p is small relative to critical press .
(pc) PR >
-
is small
isobars
initial eg
Thermal eff= networ =
1- [t] 1 always (u) internal
energy
① point
of boil-first bubblese
Wifpar
molar based
(h) enthalpy is
② last
drop of water alles
-




Du =
Q -

W PV RT =




Process Au Q W Ideal Isocaric
gas




·
Isobaric Q -

P(Vz vi) -
An + w P(ve-vi) w = P(V =

v. ) w =
PV-PV ,


const P w =
RT - RT

bar x18 Pa
J
=


Isothermal sn
f(T) W Q w= , (n
PV [i]
IPa IN/m ?
=
.
=
const Temp O RT In[k/vis
heat flaw
.
w =




CVAT tables
Isocaric/Isovolumetric Q =




5/kg K
molar based
O
FCV(TdT
·




const Volume Q Su it ,
5




(g) 5/1g
#




Q = mCUST w = 0 Pa =
-
-




Udiabatic inf ⑧ AU su
Spar Ibax10" N/m2
-
-
=




(52 5 ]
=
const G
=
w Cu ·

,




/ Par RT . [] #
(1b] IMPa 4bar
Poly tropic
Au + W W = =
tables w = ·


n= 1


pun
= const w= PlV i (n()
n= 1 w =
PV In 1
1000
enthalpy
, n =



PV-PV V. [Vz P24P entry
qualitydensitytemp
,
RTz-RTi Expansion
,
n> w =
w =
:

1 n n > 1
Compression V, V P2) Pi
-

-
n :