# 1.6 Mechanisms of heat transfer  (Page 17/27)

 Page 17 / 27

(a) An exterior wall of a house is 3 m tall and 10 m wide. It consists of a layer of drywall with an R factor of 0.56, a layer 3.5 inches thick filled with fiberglass batts, and a layer of insulated siding with an R factor of 2.6. The wall is built so well that there are no leaks of air through it. When the inside of the wall is at $22\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ and the outside is at $-2\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , what is the rate of heat flow through the wall? (b) More realistically, the 3.5-inch space also contains 2-by-4 studs—wooden boards 1.5 inches by 3.5 inches oriented so that 3.5-inch dimension extends from the drywall to the siding. They are “on 16-inch centers,” that is, the centers of the studs are 16 inches apart. What is the heat current in this situation? Don’t worry about one stud more or less.

For the human body, what is the rate of heat transfer by conduction through the body’s tissue with the following conditions: the tissue thickness is 3.00 cm, the difference in temperature is $2.00\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , and the skin area is $1.50\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ . How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)

The rate of heat transfer by conduction is 20.0 W. On a daily basis, this is 1,728 kJ/day. Daily food intake is $2400\phantom{\rule{0.2em}{0ex}}\text{kcal/d}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}4186\phantom{\rule{0.2em}{0ex}}\text{J/kcal}=10,050\phantom{\rule{0.2em}{0ex}}\text{kJ/day}$ . So only 17.2% of energy intake goes as heat transfer by conduction to the environment at this $\text{Δ}T$ .

You have a Dewar flask (a laboratory vacuum flask) that has an open top and straight sides, as shown below. You fill it with water and put it into the freezer. It is effectively a perfect insulator, blocking all heat transfer, except on the top. After a time, ice forms on the surface of the water. The liquid water and the bottom surface of the ice, in contact with the liquid water, are at $0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ . The top surface of the ice is at the same temperature as the air in the freezer, $-18\phantom{\rule{0.2em}{0ex}}\text{°}\text{C.}$ Set the rate of heat flow through the ice equal to the rate of loss of heat of fusion as the water freezes. When the ice layer is 0.700 cm thick, find the rate in m/s at which the ice is thickening.

An infrared heater for a sauna has a surface area of $0.050\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ and an emissivity of 0.84. What temperature must it run at if the required power is 360 W? Neglect the temperature of the environment.

620 K

(a) Determine the power of radiation from the Sun by noting that the intensity of the radiation at the distance of Earth is $1370\phantom{\rule{0.2em}{0ex}}{\text{W/m}}^{2}$ . Hint: That intensity will be found everywhere on a spherical surface with radius equal to that of Earth’s orbit. (b) Assuming that the Sun’s temperature is 5780 K and that its emissivity is 1, find its radius.

## Challenge problems

A pendulum is made of a rod of length L and negligible mass, but capable of thermal expansion, and a weight of negligible size. (a) Show that when the temperature increases by dT , the period of the pendulum increases by a fraction $\alpha LdT\text{/}2$ . (b) A clock controlled by a brass pendulum keeps time correctly at $10\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ . If the room temperature is $30\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , does the clock run faster or slower? What is its error in seconds per day?

Denoting the period by P , we know $P=2\pi \sqrt{L\text{/}g}.$ When the temperature increases by dT , the length increases by $\alpha LdT$ . Then the new length is a. $P=2\pi \sqrt{\frac{L+\alpha LdT}{g}}=2\pi \sqrt{\frac{L}{g}\left(1+\alpha dT\right)}=2\pi \sqrt{\frac{L}{g}}\left(1+\frac{1}{2}\alpha dT\right)=P\left(1+\frac{1}{2}\alpha dT\right)$
by the binomial expansion. b. The clock runs slower, as its new period is 1.00019 s. It loses 16.4 s per day.

What is mean electric potential
Electric density formula
Int E•dA
Vineet
what is relation betweeen potential energy of a system and work done in bringing last chaege from infinity
Einstein and his general theory of relativity, a very nice concept,which revolutionize our modern world.
what's the theory of relativity?
Piyali
it related to universe time period
jyotirmayee
it is a theory in which time is taken as relative,for diff. motion of objects.
Antares
no !!!
jyotirmayee
it is E=mc'square
jyotirmayee
what is black hole?
jyotirmayee
E=mc^2 is just a reln which sums up everything dude
Antares
what does e=mc^2 stand for?explain
Piyali
m not dude
jyotirmayee
e for speed of light
jyotirmayee
c for speed of light
jyotirmayee
m for mass of object
jyotirmayee
black hole is a super massive object in space gravitation pull of which s so strong dt evn light cannot escape. John wheeler 1st detected it, n concept of it ws given by Einstein himself from his general theory of relativity. Basically v cn si 3 types of it super massive, interstellar n intermediate
Antares
which topic now u studying?
jyotirmayee
e defined? sorry it,s wrong
jyotirmayee
Why?
Arzoodan
how black holes r formed?
Piyali
e is not speed of light
jyotirmayee
black holes formed when the centre of very massive star collapsed itself
jyotirmayee
e is energy.
Antares
what do u mean by quantum mechanics?
jyotirmayee
in most of d cases black holes r formed by massive collapsed star or star system
Antares
sahoo u don't seem to understand relative physics, plz study that first.
Antares
exatly...
Arzoodan
Apollo is the name of a satellite !!!!!
jyotirmayee
quantum mechanics is d study of physics describing nature at d smallest level of energy of atoms n subatomic particles.
Antares
qm means explains about the microscopic particles..
KRANTHI
nope name of d sun god
Antares
why the mercury used in thermometers?
jyotirmayee
Ali brother ur exactly spelling is wrong,,,,,
jyotirmayee
why the colour of tube light white?
jyotirmayee
why the mouth became red colour ,,by the regular eating of leaf called ,,betel combining with areca?
jyotirmayee
all formula for calculate specific latent heat of any substance
hello
Nigar
Hi, your real Nigga...? Or this jock?
Arzoodan
real
Nigar
You from Pakistan or India?
Arzoodan
c'mon guys.. let's talk Physics.
Yoblaze
mass multiplied with latent heat of a substance
Yoblaze
Arzoodan
you both?
jyotirmayee
in which class?
jyotirmayee
physics is the only subject which underestimated chemistry ,,bio
jyotirmayee
how capacitor is made in inst?
Piyali
what is dipole moment
it is the product of electric charges and distance between the two charges
Shikhar
Arzoodan
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
brad is separation and distance ,are they different?
Ssempala
What is dielectric
its a type of medium. generally poor conductors. but their conductivity can be changed
vedanth
you just have to add impurities
vedanth
Thanks
Ssempala
grt
Ssempala
a material which behave as conductor
Shikhar
insulating material, energy level for electron transfer is very high e.g used to increase a magnetic field in a capacitor
What is the difference between specific heat capacity and heat capacity? Give the equations
presentation on power
relation between Celsius and Kelvin
0" degree Celsius=273kelvin
jyotirmayee
Newton's second laws is call with
what is mean by thermodynamics
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
show mathematically that an electron has the greater speed than the proton when they attract each other
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar
what is electrostatics
the study of charge at rest
Gulzar
@Hero; the study of charges at rest is the electrostatics
Sikandar
okay what is electrostatic?
Abd
charge at rest
Nawal
set of character...
Arzoodan
oky
Abd
Gauss law, electric fields, dipoles,...
Antonio
good
Abd