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Strategy

Heat is used to raise the temperature of air so that Q = mc Δ T . The rate of heat transfer is then Q / t , where t is the time for air turnover. We are given that Δ T is 10 . C , but we must still find values for the mass of air and its specific heat before we can calculate Q size 12{Q} {} . The specific heat of air is a weighted average of the specific heats of nitrogen and oxygen, which gives c = c p 1000  J/kg ⋅º C from [link] (note that the specific heat at constant pressure must be used for this process).

Solution

  1. Determine the mass of air from its density and the given volume of the house. The density is given from the density ρ size 12{ρ} {} and the volume
    m = ρV = 1 . 29 kg/m 3 12 . 0 m × 18 . 0 m × 3.00 m = 836 kg. size 12{m= ital "pV"= left (1 "." "29"`"kg/m" rSup { size 8{3} } right ) left ("12" "." 0`m times "18" "." 0`m times 3 "." 0`m right )="836"`"kg"} {}
  2. Calculate the heat transferred from the change in air temperature: Q = mc Δ T size 12{Q= ital "mc"ΔT} {} so that
    Q = 836 kg 1000 J/kg ⋅º C 10.0º C = 8 . 36 × 10 6 J. size 12{Q= left ("836"" kg" right ) left ("1000 J/kg" cdot °C right ) left ("10 "°C right )" =8" "." "36" times "10" rSup { size 8{6} } `J} {}
  3. Calculate the heat transfer from the heat Q size 12{Q} {} and the turnover time t size 12{t} {} . Since air is turned over in t = 0 . 500 h = 1800 s size 12{t=0 "." 5`h="1800"`s} {} , the heat transferred per unit time is
    Q t = 8 . 36 × 10 J 1800  s = 4 . 64 kW. size 12{ { {Q} over {t} } = { {8 "." "36" times "10" rSup { size 8{6} } `J} over {"1800"`s} } =4 "." 6`"kW"} {}

Discussion

This rate of heat transfer is equal to the power consumed by about forty-six 100-W light bulbs. Newly constructed homes are designed for a turnover time of 2 hours or more, rather than 30 minutes for the house of this example. Weather stripping, caulking, and improved window seals are commonly employed. More extreme measures are sometimes taken in very cold (or hot) climates to achieve a tight standard of more than 6 hours for one air turnover. Still longer turnover times are unhealthy, because a minimum amount of fresh air is necessary to supply oxygen for breathing and to dilute household pollutants. The term used for the process by which outside air leaks into the house from cracks around windows, doors, and the foundation is called “air infiltration.”

A cold wind is much more chilling than still cold air, because convection combines with conduction in the body to increase the rate at which energy is transferred away from the body. The table below gives approximate wind-chill factors, which are the temperatures of still air that produce the same rate of cooling as air of a given temperature and speed. Wind-chill factors are a dramatic reminder of convection’s ability to transfer heat faster than conduction. For example, a 15.0 m/s wind at C has the chilling equivalent of still air at about 18º C .

Wind-chill factors
Moving air temperature Wind speed (m/s)
ºC size 12{ left (°C right )} {} 2 size 12{2} {} 5 size 12{5} {} 10 size 12{ bold "10"} {} 15 size 12{ bold "15"} {} 20 size 12{ bold "20"} {}
5 size 12{5} {} 3 size 12{3} {} 1 size 12{ - 1} {} 8 size 12{ - 8} {} 10 size 12{ - "10"} {} 12 size 12{ - "12"} {}
2 size 12{2} {} 0 size 12{0} {} 7 size 12{ - 7} {} 12 size 12{ - "12"} {} 16 size 12{ - "16"} {} 18 size 12{ - "18"} {}
0 size 12{0} {} 2 size 12{ - 2} {} 9 size 12{ - 9} {} 15 size 12{ - "15"} {} 18 size 12{ - "18"} {} 20 size 12{ - "20"} {}
5 size 12{ - 5} {} 7 size 12{ - 7} {} 15 size 12{ - "15"} {} 22 size 12{ - "22"} {} 26 size 12{ - "26"} {} 29 size 12{ - "29"} {}
10 size 12{ - bold "10"} {} 12 size 12{ - "12"} {} 21 size 12{ - "21"} {} 29 size 12{ - "29"} {} 34 size 12{ - "34"} {} 36 size 12{ - "36"} {}
20 size 12{ - bold "20"} {} 23 size 12{ - "23"} {} 34 size 12{ - "34"} {} 44 size 12{ - "44"} {} 50 size 12{ - "50"} {} 52 size 12{ - "52"} {}
40 size 12{ - bold "40"} {} 44 size 12{ - "44"} {} 59 size 12{ - "59"} {} 73 size 12{ - "73"} {} 82 size 12{ - "82"} {} 84 size 12{ - "84"} {}

Although air can transfer heat rapidly by convection, it is a poor conductor and thus a good insulator. The amount of available space for airflow determines whether air acts as an insulator or conductor. The space between the inside and outside walls of a house, for example, is about 9 cm (3.5 in) —large enough for convection to work effectively. The addition of wall insulation prevents airflow, so heat loss (or gain) is decreased. Similarly, the gap between the two panes of a double-paned window is about 1 cm, which prevents convection and takes advantage of air’s low conductivity to prevent greater loss. Fur, fiber, and fiberglass also take advantage of the low conductivity of air by trapping it in spaces too small to support convection, as shown in the figure. Fur and feathers are lightweight and thus ideal for the protection of animals.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
Berger describes sociologists as concerned with
Mueller Reply
what is hormones?
Wellington
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Source:  OpenStax, Physics subject knowledge enhancement course (ske). OpenStax CNX. Jan 09, 2015 Download for free at http://legacy.cnx.org/content/col11505/1.10
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