TITLE.PM5

452 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th10-1.pm5

i.e., μ=

W

Ws ...(10.6)

where, Ws = Specific humidity of air when air is fully saturated

∴ μ=

0 622

0 622

.

.

()

()

p

pp

p

pp

pp p

pp p

v

tv

vs

tvs

vt vs

vs t v

−

F

HG

I

KJ

−

F

HG

I

KJ

=

−

−

=

−

F

HG

I

KJ

−

F

HG

I

KJ

L

N

M

M

M

M

M

O

Q

P

P

P

P

P

p

p

p

p

p

p

v

s

vs

t

v

t

1

1

...(10.7)

where pvs = Partial pressure of water vapour when air is fully saturated (pvs can be calculated
from steam tables corresponding to the dry bulb temperature of the air).
Relative humidity (RH), φ :

Relative humidity, φ=Mass of water vapour in a given volume

Mass of water vapour in the same

volume if saturated at the same temp.

==m =

m

pT

RT

pT

RT

p

vs p

v

v

vs

v

v

vs ...(10.8)

Inserting the value of equation (10.8) into equation (10.7), we get

μφ φ φ φ

φ

=

−

−

L

N

M

M

M

M

O

Q

P

P

P

P

=

−

−

L

N

M

M

M

M

O

Q

P

P

P

P

= −

−

F

HG

I

KJ

1

1

1

1

p

p

p

p

p

p

p

p

pp

pp

vs

v

v

t

vs

t

vs

t

tvs

tvs

∴ φ(pt – pvs) = μ(pt – φ pvs)
or φ(pt – pvs + μpvs) = μpt

∴ φ μ

μ

μ

μ

=

−+

=

−−

p

pp p p

p

t

tvs vs vs

t

11 ()

...(10.9)

Since pvs << pt

∴φ ~− μ

Inserting the value of the pv from equation (10.4) into equation (10.8), we get

φ =

pW

p

a

(^0622) vs
1
.
× = 1.6 W
p
p
a
vs
...(10.10)
Note 1. Relative humidity as compared to specific humidity plays a vital role in comfort air-conditioning and
industrial air-conditioning. Relative humidity signifies the absorption capacity of air. If initial relative humidity of
air is less it will absorb more moisture.

2. W, μ and φ cannot be conveniently measured as they require measurement of pv and pvs. The value
   of pv can be obtained from the measurement of the wet bulb temperature and the value of pvs can be calculated
   from steam tables corresponding to given air temperature.