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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

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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Uday
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Ramkumar Reply
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Sravani Reply
what is system testing?
AMJAD
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
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The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
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Source:  OpenStax, College physics: physics of california. OpenStax CNX. Sep 30, 2013 Download for free at http://legacy.cnx.org/content/col11577/1.1
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