Psychrometry
1 Humidity
We are studying systems involving both dry air and water vapour. Water vapour is in the atmosphere
all around us and its amount depends on conditions.
Water vapour is not included in the composition of dry air, and we talk about wet air as a mixture of
dry air and water vapour.
As engineers were primarily interested in applications relating to Heating, Ventilation, Air Conditioning.
HVAC.
We will treat wet air as a mixture of two ideal gasses.
.
1 Da Air Ra = 2875kg K
2
. Water vapour Rv = 861 .
5
JugK
The total in the mixture p is the sum of the partial pressures of dry air P(a), and the partial pressure
of water vapour P(v). I.e.
P =
Pa +
Pr
The partial pressure of water vapour is usually referred to as the vapour pressure.
How much water vapour is in this room?
We have a mass of dry air Ma , and we have a mass of water vapour Mv .
We define the specific humidity or the absolute humidity or the humidity ratio to be
=
w
=
Here V is the volume of wet air being considered.
This humidity has units of kg of water vapour per kg of dry air, and is not measured in percentages.
As both the dry air and the water vapour are ideal gases we can write
=
w
Eliminating Pa in favour of p and pr we find:
Rape
Ra
As
w = = 0 .
02 w = 0 .
622 Pr
Rv(p - pr) p-pr
If the air is dry, then m(v) = 0 and the vapour pressure p(v) = 0, and therefore We =0
Ky War Vapour
ky dig Al2
, 1.1 Specific humidity example
Leis suppose Pa 1000000 Pa wa 1000 Pa
=
pr =
With This p =
Pa + Pr = 101000 Pa AND
W = Rapu = 0 .
0062
kg water vapour
Rv(p-pr( kg dry Alz
1.2 Saturation pressure of water
If you are sitting in a room surrounded by dry air and water vapour, then you cannot keep increasing
the amount of water vapour in the atmosphere indefinitely.
There is an upper limit on the vapour pressure, called the saturation pressure for water vapour or
saturation vapour pressure. This is the maximum partial pressure of water vapour you can have in the
atmosphere before it starts condensing to form liquid water.
The saturation vapour pressure is a function of temperature
At 25^C, the saturation vapour pressure - Pg 3169 8 =
.
Pa
Values for other temperature can be obtained from the steam tables.
The specific humidity at saturation is obtained by replacing the vapour pressure P , with the vapour
pressure at saturation Pg , in our definition of specific humidity i.e.,
Wg = Wint =
Ra Pg
Rv(p Pg) -
1.3 Relative humidity
The relative humidity is defined to be the ratio of the mass of water vapour in the air, to the mass of
water vapour in the air at saturation, i.e., phill or o
U MVVMg =
This is dimensionless and is either expressed as a decimal, or more commonly as a percentage.
Human comfort is affected by the amount of water vapour in the atmosphere and typically relative
humidity in air conditioned environment is set to 45% +/- 10% to make occupants comfortable.
9 mr
g-V- Ru
= =
Mg 99X Pg
We can use this to relate the relative humidity to the specific humidity. Recall -
W = RaP = X RaOPs
Rv(p- p) Rv(p-ppg)
Rearranging this expression - w-Rr(p Opg)-
= Ra & Pg
=> wRup = (wRv + Rc) py &
Therefore - &
=whi w) pe
1 Humidity
We are studying systems involving both dry air and water vapour. Water vapour is in the atmosphere
all around us and its amount depends on conditions.
Water vapour is not included in the composition of dry air, and we talk about wet air as a mixture of
dry air and water vapour.
As engineers were primarily interested in applications relating to Heating, Ventilation, Air Conditioning.
HVAC.
We will treat wet air as a mixture of two ideal gasses.
.
1 Da Air Ra = 2875kg K
2
. Water vapour Rv = 861 .
5
JugK
The total in the mixture p is the sum of the partial pressures of dry air P(a), and the partial pressure
of water vapour P(v). I.e.
P =
Pa +
Pr
The partial pressure of water vapour is usually referred to as the vapour pressure.
How much water vapour is in this room?
We have a mass of dry air Ma , and we have a mass of water vapour Mv .
We define the specific humidity or the absolute humidity or the humidity ratio to be
=
w
=
Here V is the volume of wet air being considered.
This humidity has units of kg of water vapour per kg of dry air, and is not measured in percentages.
As both the dry air and the water vapour are ideal gases we can write
=
w
Eliminating Pa in favour of p and pr we find:
Rape
Ra
As
w = = 0 .
02 w = 0 .
622 Pr
Rv(p - pr) p-pr
If the air is dry, then m(v) = 0 and the vapour pressure p(v) = 0, and therefore We =0
Ky War Vapour
ky dig Al2
, 1.1 Specific humidity example
Leis suppose Pa 1000000 Pa wa 1000 Pa
=
pr =
With This p =
Pa + Pr = 101000 Pa AND
W = Rapu = 0 .
0062
kg water vapour
Rv(p-pr( kg dry Alz
1.2 Saturation pressure of water
If you are sitting in a room surrounded by dry air and water vapour, then you cannot keep increasing
the amount of water vapour in the atmosphere indefinitely.
There is an upper limit on the vapour pressure, called the saturation pressure for water vapour or
saturation vapour pressure. This is the maximum partial pressure of water vapour you can have in the
atmosphere before it starts condensing to form liquid water.
The saturation vapour pressure is a function of temperature
At 25^C, the saturation vapour pressure - Pg 3169 8 =
.
Pa
Values for other temperature can be obtained from the steam tables.
The specific humidity at saturation is obtained by replacing the vapour pressure P , with the vapour
pressure at saturation Pg , in our definition of specific humidity i.e.,
Wg = Wint =
Ra Pg
Rv(p Pg) -
1.3 Relative humidity
The relative humidity is defined to be the ratio of the mass of water vapour in the air, to the mass of
water vapour in the air at saturation, i.e., phill or o
U MVVMg =
This is dimensionless and is either expressed as a decimal, or more commonly as a percentage.
Human comfort is affected by the amount of water vapour in the atmosphere and typically relative
humidity in air conditioned environment is set to 45% +/- 10% to make occupants comfortable.
9 mr
g-V- Ru
= =
Mg 99X Pg
We can use this to relate the relative humidity to the specific humidity. Recall -
W = RaP = X RaOPs
Rv(p- p) Rv(p-ppg)
Rearranging this expression - w-Rr(p Opg)-
= Ra & Pg
=> wRup = (wRv + Rc) py &
Therefore - &
=whi w) pe
