quiz

Chapter Two

Handout Five

Thermodynamic Processes in Buildings There are eight properties of air needed in buildings and in HVAC systems:

1. Pressure (P) force per unit area measured in kPa

The pressures of air and water are very important.

– Absolute pressure (Pabs): pressure exerted by fluid above zero pressure (vacuum)

– Gage pressure (Patm): pressure exerted by fluid above atmospheric pressure patm = 101 kPa

at sea level

– Vacuum pressure (Pvac): pressure exerted by fluid below atmospheric pressure patm

Pressure Effect on Properties

Pressure Effect on Properties

Atmospheric Layers

Note: Height of Mount Everest is 8.848 km

Unlike the Ocean, there is no definite boundary. The atmosphere gradually thins out as you get higher, at a rate of roughly 1% per hundred meters for the first few thousand meters, more slowly after that. About half the mass of the atmosphere is within the first 5.5 km, about three quarters within 11 km.

The atmosphere is breathable for people in normal health up to about 4 km, about the elevation of the highest cities towns, for example Lhasa in Tibet at 3,656 m, after which it becomes difficult without acclimatization. No doubt by coincidence, the Summit of Earth's highest Mountain, Everest, at 8.8 km, seems to be pretty close to the boundary where a very fit person can survive without oxygen equipment, at least for a short time.

Nearly all weather occurs in the lowest layer of the atmosphere, the troposphere, extending to about 12 km (higher at the equator, lower at the poles). Above that, there are several layers with their own distinct properties.

The Kármán line, located at 100 km, considered to be the boundary of outer space, beyond which a traveller is considered to be an astronaut. This isn't entirely arbitrary. It approximates the height beyond which no aircraft flight would be possible because the atmosphere is too thin to provide aerodynamic lift at a speed below orbital velocity.

ratio of height of atmosphere to diameter of Earth

Pabs = Patm + Pg

Pabs = Patm - Pvac

Components in dry air Volume ratio = Molar ratio,

compared to dry air Molar Mass Molar mass in air

Name Formula [mol/molair] [vol %] [g/mol]

[kg/kmol] [g/molair]

[kg/kmolair] [wt %]

Nitrogen N2 0.78084 78.084 28.013 21.873983 75.52

Oxygen O2 0.20946 20.946 31.999 6.702469 23.14

Argon Ar 0.00934 0.934 39.948 0.373114 1.29

Carbon dioxide CO2 0.00033 0.033 44.010 0.014677 0.051

Neon Ne 0.00001818 0.001818 20.180 0.000367 0.0013

Helium He 0.00000524 0.000524 4.003 0.000021 0.00007

Components in dry air Volume ratio = Molar ratio,

compared to dry air Molar Mass Molar mass in air

Name Formula [mol/molair] [vol %] [g/mol]

[kg/kmol] [g/molair]

[kg/kmolair] [wt %]

Methane CH4 0.00000179 0.000179 16.042 0.000029 0.00010

Krypton Kr 0.0000010 0.0001 83.798 0.000084 0.00029

Hydrogen H2 0.0000005 0.00005 2.016 0.000001 0.000003

Xenon Xe 0.00000009 0.000009 131.293 0.000012 0.00004

Average molar mass of air 28.9647

Gibbs Dalton law:

Mixture Pressure = Sum of the partial pressures of the constituents

For moist-air:

All dry gases can be considered as one gas, then:

2. Temperature (T): A measure of the thermal activity in a body measured in

• Thermal activity depends on the velocity of the molecules and other particles of which a

matter is composed.

• Thermometer is used to measure temperature

– rely on the fact that most liquids expand and contract when their temperature is raised or

lowered

• Temperature scale: Fahrenheit (˚F) and Celsius (˚C), Rankine (˚R) and Kelvin

– Fahrenheit • 0°F as the stabilized

temperature when equal amount of ice, water, and salt are mixed

– Celsius • 0°C as melting point of ice

(water) and 100°C as boiling point of water

• ˚ F = 1.8 ˚ C + 32 – Kelvin

• 0 K as absolute zero • K = ˚ C + 273.15

– Rankine • ˚ R = ˚ F + 459.67

a. Dry-bulb temperature (Td): The dry-bulb temperature (DBT) is the temperature of air measured

by a thermometer freely exposed to the air but shielded from radiation and moisture. DBT is the

temperature that is usually thought of as air temperature, and it is the true thermodynamic

temperature. It indicates the amount of heat in the air and is directly proportional to the mean

kinetic energy of the air molecules. Temperature is usually measured in degree Celsius (°C),

Kelvin (K), or Fahrenheit (°F) in IP units.

Unlike wet bulb temperature, dry bulb temperature does not indicate the amount of moisture in

the air. In construction, it is an important consideration when designing a building for a certain

climate. Niall called it one of "the most important climate variables for human comfort and

building energy efficiency.

b. Wet-bulb temperature (Tw): The thermodynamic wet-bulb temperature is the lowest temperature

which may be achieved by evaporative cooling of a water-wetted (or even ice-covered),

ventilated surface.

c. Dew-point temperature (Tdew): the dew point is the temperature to which the ambient air must

be cooled to reach 100% relative humidity assuming there is no evaporation into the air; it is the

point where condensate (dew) and rain would form.

Dry-bulb and Wet-bulb Temperatures

Water absorbs heat from the probe (bulb)-in fact from the air- as it evaporates. If the weather is dry, more

water evaporates and thus absorbs more heat from the bulb- then the temperature difference between

dry and wet becomes large. If the weather is wet, less water will evaporate and thus absorbs less heat

from the bulb- then the temperature difference between dry and wet becomes little. At 100% relative

humidity, the wet-bulb temperature equals the dry-bulb temperature.

In a weather station, the thermometer is usually housed in a Stevenson Screen. A Stevenson Screen is a white boxed shelter that contains temperature and relative humidity equipment. It shields the instruments from sunshine and precipitations and has louvered sides to permit the free movement of air. Ideally the shelter is placed over grass, mounted at 1 meter above the ground and as far from any buildings as circumstances permit.

3. Humidity

a. Humidity Ratio (W)

Units: dimensionless

gwv/gda

gwv/kgda

b. Relative Humidity (φ)

Units: percentage

What is the difference between humidity ratio and relative humidity and why do we use relative humidity

in weather forecast not humidity ratio?

Conduct the experiment: bring four different sizes of bakers and record both W and in the table below:

Take W for the room as 8 gwv/kgda

Humidity Ratio (W) 8 gwv/kgda 8 gwv/kgda 8 gwv/kgda 8 gwv/kgda 8 gwv/kgda

Relative Humidity ( 100% (rest is

rain) 100% 50% 30% 10%

Heating

Cooling

Relationship between Temperature and Relative Humidity During the Day

Relative humidity ( ) is inversely proportional to the air temperature .i.e. if temperature increases, the

Relative humidity decreases and vice versa.

Effect of Relative Humidity

Room humidity can have a major impact on the quality of the living environment. A relative humidity ( )

of 40-60% is generally considered to be optimal for a comfortable and healthy home. Too much moisture

can lead to mold and overheating. Too little causes dry eyes, chapped lips and an environment in which

bacteria and viruses can thrive.

4. Specific volume (ʋ) (which is the reciprocal of density) measured in m 3 /kg

Density – mass/volume (used for solids and liquids)

air =1.2 kg/m 3 , water = 1000 kg/m

3  Ratio= 833

Changes slightly with temperature, why? Because of volume change

5. Specific Heat (c)

 Amount of heat that is required to change the temperature of 1 kg of the substance

1 °C.

 Units (J/kg-°C)

 Without phase change !!

 Property of material which changes slightly with temperature

Specific heat for water is 4.186 kJ/(kg-K)

air is 1.00 kJ/(kg-K)

6. Specific internal energy (μ) measured in kJ/kg

• Internal energy (U): microscopic energy possessed by a system caused by the

motion/vibration of the molecules and/or intermolecular forces.

- the motion/vibration increases with temperature

• Internal energy is thus often measured by the body’s temperature (this is not

true when the body is a liquid or a solid (such as ice) which is changing phase!)-

this leads to sensible and latent heat discussed later

Important: a body does not contain heat; it contains thermal energy

7. Specific Enthalpy (h) measured in kJ/kg

Can be defined as the energy per unit mass a fluid transports across a system boundary.

– A property of a body that measures its heat content

– Enthalpy includes: (i) Internal energy U and

(ii) pv or energy due to flow work

Which is internal energy + work needed to move a mass of fluid across a system boundary.

– Enthalpy is a combined property which is widely used in thermal analysis

– When T, p or V changes, H changes

specific enthalpy h = u + p.v in kJ/kg (v is specific volume=1/density)

Instead of sensible or latent heat equations, enthalpy equation is widely used since one does not have to

worry about state of fluid.

Enthalpy is the total energy (sensible + latent)

8. Specific entropy (s). not need in this course.

Two other properties needed:

Specific heat at constant volume (cv)

Specific heat at constant pressure (cp)

There are two sourced to obtain properties of air:

1. Simple equations such as the ideal gas law (for air, or moist air).

2. Tables computed from complex equations (for water and refrigerants).

Sensible and Latent Heats

Note to consider from the chart

1. Since the air is a mixture of dry gases and water vapor, the water vapor carries the latent heat,

while the dry gases carries the sensible heat.

2. Sensible heat is a function of temperature f(T), while latent heat is a function of humidity ratio

f(W).

3. The total enthalpy of the moist-air (hT) = enthalpy of dry-air (hda)+ enthalpy of water vapor (hwv).

4. To convert 1 pound of water from solid to liquid you need 144 Btu. But to convert the same

amount from liquid to gas you need 970 Btu. That is 6.7 times (970/144). What does this mean?

Water vapor carries a huge amount of energy

Ideal Gas Law

The ratio of pressure P times molar volume ʋ divided by the absolute temperature T is observed to

approach a constant value, when the pressure is allowed to approach zero.

Where R is the universal gas constant = 8314.41 J/(kg.mol.K)

The gas constant R = R/Molecular weight of gas

For example: Rair= 8314.41/28.97 = 287 J/(kg.K)

Mole: the standard unit to measure the amount of a substance.

Avogadro’s principle: Equal volumes of all gases at the same temperature and pressure contain the same

number of molecules (6.023 *10 23

molecules). That is, one mole of a substance contains 6.023 *10 23

molecules.

P=Rair*T

P=Rair*T

P=(m/V) Rair*T

PV=m×Rair×T

Since mass of substance (m) = number of moles in kmol (n) * molecular weight of the substance (M)

Then, PV= n*M* Rair *T

Also Rair =R/M, then M=R/Rair where R is the universal gas constant =8314.41 J/(kg.mol.K)

For example Rair = 8314.41/28.97= 287 J/(kg.K)

Then, PV =n*(R/Rair)*Rair*T =n*R*T

Forms of the Ideal Gas Law:

TRP air

TmRPV air

nRTPV  (not used in HVAC)

Where;

P= pressure, Pa

ʋ= specific volume, m 3 /kg

Rair= gas constant of air = 287 J/(kg.K)

T = absolute temperature, K

V = volume, m 3

M = mass, kg

Relationship between Humidity ratio and Pressure:

From above, since TmRPV air

Since Rgas= universal gas constant (R)/ molecular weight (Mgas), and Patm= Pda + Pwv

Then,

Example:

The dimensions of your classroom is 12 m × 6 m × 3 m. If the temperature (Td) is 22 o C, and the humidity

ratio is 10 gwv/kgda, answer the following questions.

1. Use the ideal gas law to calculate the density (ρ) of air in the classroom.

2. Calculate the mass of water vapor and the mass of dry air in the classroom.

First find Pwv and Pda and then use the ideal gas law equation:

Note that volume and temperature of both dry air and water vapor is the same.

From above relationship:

Pda= Patm -Pwv=101.3-1.6=99.7 kPa

Note that Rair =287.05 J/(kg.K)

And Rwv= 461.52 J/(kg.K)

Zi

W

Q

mi

Vi

Pi

Ui

Hi

Mo

Vo

Po

Uo

Ho

System

Zo

Open-system First Law of Thermodynamics:

.2..2.

22 Wh

V zgmQh

V zgm o

o ooi

i ii 







 



 

 





 



 

Q = heat transfer rate, W

M = mass flow rate, kg/s

Ho= final enthalpy, kJ/kg

Hi = initial enthalpy, kJ/kg

To = final temperature, K

Ti = initial temperature, K

Cp = specific heat of air =1006 J/(kg.K)

Important Note

Is heat gain to air

Is heat removal from air

UA is equivalent to m-dot cp

Example 1:

Air enters an auditorium through the diffusers of an HVAC system at a temperature of 12 o C at a

volumetric flow rate of 0.5 m 3 /s. The air collects the heat and leaves through the air inlets at the set-point

temperature of the space at T=24 o C. Calculate the following:

1. the air mass flow rate entering the auditorium.

2. the heat removed from the auditorium?

Air enters at 12 o C, carries the heat and leaves at 24

o C, then the amount 0f heat removed by air as it

leaves:

Example 2

In a windy day in Bahrain (sea level, Patm=101.325 kPa, ρ=1.2 kg/m 3 ), air leaks to a building at a rate of 1

air change per hour. All air in the building is exchanged with fresh air every one hour “once each hour”. It

occurs through cracks, around windows, through loose fittings building materials, open doors, etc… This is

called infiltration. Take the outdoor temperature (To) is 39 o C and the area of the building is 150 m

2 , with

an average height of 7 m and answer the following questions:

1. Calculate the volumetric flow rate (Vinf) of this infiltrating air.

Air change per hour (ACH) = (V) Volume

V)( Rate Flow Volumetric .

2. Calculate the mass flow rate (minf) of this infiltrating air

3. How much heat must the cooling system of the building remove from this infiltrating air to keep

the building at its set-point indoor temperature (Ti) of 22 o C.

4. How many refrigeration tons does this heat equal to? Comment on the answer and draw a

conclusion.

1 ton refrigeration is = 3.517 kW (refer to conversion factors sheet)

Then,

Comment: a small quantity of air leaking through windows causes a lot of heat

gain that the HVAC systems has to remove. In hot climates, buildings must be air-

tight. Windows has two basic functions: daylight and view.