Figure 2.10 shows the relationship between the three phases of water; solid, liquid Temperature Fig. 2.10 The triple point of water. The triple point

And vapour, as changes of pressure and temperature occur. The triple point at 0.01°C (273.16 K) and 613.2 Pa is defined by international agreement as the temperature at which the solid, liquid and vapour forms of water can exist together in saturated equilibrium. As a matter of interest, a consequence of this definition for the Celsius scale of temperature is that the ice point and the steam point are determined experimentally and are not precisely 0°C (273.15 K) and 100°C (373.15 K), respectively.

We see in the figure that it is not possible for liquid water to exist at a pressure below that of the triple point. We also see that, because the solid-liquid line is very nearly vertical, liquid water temperatures less than 0°C are only possible at very high pressures.

Exercises

1. (a) Air at a condition of 30°C dry-bulb, 17°C wet-bulb and a barometric pressure of 105 kPa enters a piece of equipment where it undergoes a process of adiabatic saturation, the air leaving with a moisture content of 5 g kg-1 higher than entering. Calculate, using the data below, and the ideal gas laws,

(i) the moisture content of the air entering the equipment,

(ii) the dry-bulb temperature and enthalpy of the air leaving the equipment.

= 1.936 kPa = 1.015 kJ kg“1 K“1 = 1.890 kJ kg“1 K-1 = 2459 kJ kg-1 = 2500 kJ kg“1 = 6.66 x 10"1 This question.

(,b) Using the data below, calculate the moisture content of air at 17°C dry-bulb and 40 per cent saturation where the barometric pressure is 95 kPa.

Sat. vapour pressure at 17°C Specific heat of dry air Specific heat of water vapour Latent heat of evaporation at 17°C Latent heat of evaporation at 0°C Constant for psychrometric equation for wet-bulb temperatures above 0°C

Note: Psychrometric tables are not to be used for Answers

(a) (i) 6.14 g kg"1, (ii) 18°C, 46.5 kJ kg“1.

(b) 5.18 g kg“1.

2. (a) Define the following psychrometric terms

(i) Vapour pressure

(ii) Relative humidity

(iii) Humid volume

(iv) Dew point

(.b) Name two distinct types of instrument which are used to determine the relative humidity of atmospheric air and briefly explain the principle in each case.

Answer 58.93 kJ kg"1.

4. (a) Calculate the dew point of air at 28°C dry-bulb, 21°C wet-bulb and 87.7 kPa barometric pressure. Use CIBSE tables where necessary to determine saturation vapour pressure.

(b) Calculate its enthalpy.

Answers

(a) 18.11°C, (b) 66.69 kJ per kg dry air.

5. (a) Distinguish between saturation vapour pressure and the vapour pressure of moist air at an unsaturated state.

(b) Illustrate relative humidity by means of a p-V diagram for steam.

(c) What happens if air at an unsaturated state is cooled to a temperature below its dew point?

(d) Calculate the relative humidity and percentage saturation of air at 101.325 kPa, 21°C dry-bulb and 14.5°C wet-bulb (sling). You may use the CIBSE tables of psychrometric data only to determine saturation vapour pressures.

Answers

(a) 48.7%, 48.1%.

Notation

Symbol Description Unit

A surface area of a water droplet m2

Aik(T) second virial coefficient, molecules considered two m[1] kg“1

At a time

A-ijk(T) third virial coefficient, molecules considered three m3 kg’1

At a time

Aaa second virial coefficient of dry air m3 kg-1

Aww second virial coefficient of water vapour m3 kg-1

AwWW third virial coefficient of water vapour m3 kg“1

Aaw interaction coefficient m3 kg-1

A, B, C, D constants

A’, B’, etc. constants

A constant

C specific heat of moist air J kg-1 K-1

Ca specific heat of dry air J kg-1 KT1

Cs specific heat of water vapour (steam) J kg-1 K_1

Fs dimensionless coefficient

G moisture content kg per kg dry air

Gss moisture content of saturated air kg per kg dry air

Gss moisture content of saturated air at a temperature t’ kg per kg dry air

H enthalpy kJ

H specific enthalpy of moist air kJ per kg dry air

K	Enthalpy of 1 kg of dry air	KJ kg 1
Hg	Latent heat plus sensible heat in the water vapour	KJ kg’1
Associated with 1 kg of dry air
K	Enthalpy of 1 kg of water vapour at a temperature t,	KJ kg“1
	The temperature of the dry bulb	W nr2 KT1
Hc	Coefficient of heat transfer through the gas film
	Surrounding a water droplet, by convection	W nr2 K’1
K	Coefficient of heat transfer to a water droplet by radiation from the surrounding surfaces
H	= hc + hr	W m“2 K-1
Tyg	Latent heat of evaporation	KJ kg-1
(Le)	Lewis number
M	Molecular mass	Kg kmol-1
Ma	Molecular mass of dry air	Kg kmol-1
Ms	Molecular mass of water vapour (steam)	Kg kmol-1
M	Mass of gas	Kg
Ma	Mass of dry air	Kg
Ms	Mass of water vapour (steam)	Kg
«a	Number of molecules of constituent a
Nw	Number of molecules of constituent w
P	Gas pressure	N m“2, Pa or kPa
Pa	Pressure of dry air	N m-2, Pa or kPa
Pat	Atmospheric pressure (barometric pressure)	N itT2, Pa or kPa
Ps	Pressure of water vapour (steam)	N m-2, Pa or kPa
Pss	Saturation vapour pressure	N m-2, Pa or kPa
Pss	Saturation vapour pressure at the wet-bulb	N m-2, Pa or kPa
	Temperature	J kmol-1 K1
	Universal gas constant
R	Particular gas constant	J kg“1 K’1
R*	Particular gas constant of dry air	J kg"1 K-1
Rs	Particular gas constant of water vapour (steam)	J kg"1 K"1
Rss	Particular gas constant of dry saturated steam	J kg“1 K1
T	Absolute temperature	K
T	Temperature	°c
	Critical temperature	°c
Fd	Dew-point temperature	°c
‘ ss	Saturation temperature	°c
J	Wet-bulb temperature	°c
	Temperature of adiabatic saturation	°c
U	Internal energy	KJ
V	Specific volume	M3 kg-1
V	Gas volume	3 M
K	Volume of dry air	M3
Vm	Volume of 1 kmol	M3
Vs	Volume of steam	3 M
Z	Altitude above sea level	M
X	Mole fraction	KgN-1
A	Coefficient of diffusion

|i percentage saturation %

<|> relative humidity %

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