Thermodynamics Formulae

Table FI 9

9

THERMODYNAMICS FORMULAE m

Density ( p )

p = mass volume

Specific volume (v)

V- 1 ---v = volume mass m p

Specijc weight ( y )

weight - mg y=---- volume v pg

=

Virial Equations

V

P= RTI(v-B)

Continuity equation

m = c inlets

1. .

pv =

z=l+(BrPrITr) B(O)

p~~-cp~~

-

Ideal-gas Equation of State

Br = BP, I RT,

B(') = 0 . 1 3 9 - 0 . 1 7 2 1 ~ ~ ' ~

eritr

R T M

--

= 0.083- 0.422 1 T,'.~

Br = ~

( 0+(,,B(' ) )

R = universal gas constant M = molar mass of substance '

v2

v2

m e ( u , + p,v, +'+gz,)

Energy balance for an open system

Q-W

Work of steady -flow, open system

Kn = v d p + Ake + Ape

Thermal eflciency of heat engine

rl=

Coeflcient ofperformance (refrigerator)

copR =

Coeflcient ofperformane (heat pump)

c o p H P= &L!L : Kn

=

-mi ( u i + pivi + -+gzi)

2

2

I

f aw

-

Qin

Change in entropy

Qin - Qout Qii

q=-

Bn,L

TH- TL TH

COPR= 'TL TH- TL

Kn

COPm = TH TH- TL

inf rev

Change in entropyfor open system

+ s

ds0, =

~

-m s26m2 ~

rev. 0s

Change in entropyfor ideal gas

d =

j:cp$ R l n -P;I -

P2

d~

=

Isentropic Turbine Eflciency

rlr"

work of actual expansion - hl - hz. work of reversible expansion hl - h2,

Adiabatic CompressorEflciency

rlc =

work of reversible compression - h23- h work of actual compression h*o- h 1

Expression for a Reversible Process (Expansion/ Compression) in which

PVY= constant

Isothermal AU

0

Q

-nRT 1{?]

Adiabatic, c A V(2") nR -(T2-T,) Y-1

1 or -(P2V2-45) Y-1

0

Process

Q

S:fJ dV

Constant volume

m cV(TZ- T I )

0

Constant pressure

m ~ , ( T z- T I )

Constant temperature

plv1 1n4

Sf V

~ P

V(Pz - P I ) 0

P( VZ- V I )

AU

p- V-T Relations

Exponent in

mc,(Tz - T I )

--Tz - P Z TI PI

pP=C n=a

--TZ- VZ

n =0

mc,(Tz - T I )

TI plv1 I&

yl

plv1 I&

Vl

o

VI

VI

n=l

PI VI=pzvz

p1v:=pzvzl Reversible adiabatic

0

Reversible polytropic

k 01VI-PZVZ) k- 1

PlVl -pzVz k- 1

m cv

(E)

1-n

PI~I-pzvz n-1

(T2- T I )

I:* v

Constant volume

v

v

Constant pressure

01v1 -PZ~Z)

v

Tlly*pl \; v

Constant temperature

"TI= ( K ) " ' = ( ~ + I W p1VF=pzVz" -Tz - (?)*I = TI

;(

m cv(Tz - T I )

n

n-1 n#l

n=k

mcV(Tz- T I )

v

n >o

)(*l)'n

\; v

Reversible adiabatic

v

\: v

Reversible polytropic

v