High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize University Physics Textbook (Master) > Heat and Temperature

Heat Transfer: Conduction

Thermal ExpansionPrevious Section
Heat Transfer: Conductors in Series and Parallel Next Section
Popular Courses
Find My Course
0:00 / 0:00

Heat Transfer Through Conduction

  • Heat transfer through a material is called conduction.
  • Heat current in conduction has the following relation:
H=dQdt=kAΔTLH=\dfrac{dQ}{dt}=kA\dfrac{\Delta T}{L}

  • kk is the thermal conductivity of the material
  • The larger kk, the better conductor it is
  • LL is the thickness of the material
  • The thicker the material is, the less heat is transferred
  • The more area of material that can conduct heat, the more heat that is transferred
  • ΔT\Delta T is the temperature difference on both sides of the conductor
  • ΔTL\frac{\Delta T}{L} is the temperature difference per unit length and is called the temperature gradient
0:00 / 0:00

Example: Heat Transfer

The glass of a car window is rectangular in shape and has dimensions of 40 cm by 60 cm and is 3cm thick. How much heat will be transferred by conduction in 10.0 s through the glass if there is a temperature difference of 3.5º between the inner and outer surfaces? (kglass=0.84 J/m s ºC)

Solution:

A=40×60cm2A=40\times60cm^{2}

=2400cm2=0.24m2=2400cm^{2}=0.24m^{2}

L=3cmL=3cm

0.03m0.03m



ΔQ=kAΔTΔtL⇝thickness\Delta Q=\dfrac{kA\Delta T\Delta t}{L}_{{\large \rightsquigarrow}\hspace{0.2cm}\text{thickness}}

=(0.84J/ms°C)(0.24m2)(3.5°C)(10s)0.03m=\dfrac{(0.84J/ms\degree C)(0.24m^2)(3.5\degree C)(10s)}{0.03m}

=235.2J=235.2 J
Extra Practice
The glass of a car window is rectangular in shape and has dimensions of 40 cm by 60 cm and is 3cm thick. How much heat will be transferred by conduction in 10.0 s through the gas if there is a temperature difference of 3.5º between the inner and outer surfaces? (kglass=0.84 J/m s ºC)
What is the average temperature of a burning log if it releases an average of 10 kW of heat in a room at 5°C. Assume maximum emissivity for a blackened log that has a diameter of 20 cm and a length of 50 cm. (Hint: the surface area of a log has two circles as well as a rectangular part connecting these two circles. The "width" of this rectangle is the circumference of the log.)
Heat Transfer: Conduction
If object A touches object B in a thermally insulated room and heat flows from object B to object A. What can we say?
How much heat is transferred in 20 minutes across the following system? Assume all metallic parts are cubes and each side has a length of 20 cm20\ cm.
kAl=205wm⋅kkcu=385wm⋅kkBr=109wm⋅kkSt=50.2wm⋅k\begin{aligned} k_{Al}=205 \frac{w}{m\cdot k}&&k_{cu}=385 \frac{w}{m\cdot k}\\ k_{Br}=109 \frac{w}{m\cdot k} && k_{St}=50.2 \frac{w}{m\cdot k} \end{aligned}
A cubic room with a length of 4 m4\ m is isolated from the outside by a 2 cm2\ cm layer of wood and a 15 cm15\ cm layer of insulating brick.
If the temperature outside is −20°C-20\degree C, what should be the power of a heater to keep the inside temperature at 25°C25\degree C? Assume that the heat is only transferred through side walls.
We put a 2 m×1.5 m2\ m \times 1.5\ m window in one of the walls when the thickness of the glass is 2 cm2\ cm. What is the temperature inside using the same heater? (kBrick=0.15wm⋅k,kwood=0.12wm⋅k,kglass=0.8wm⋅k)(k_{Brick}=0.15 \frac{w}{m\cdot k},\quad k_{wood}=0.12 \frac{w}{m\cdot k},\quad k_{glass}=0.8\frac{w}{m\cdot k})
A solar array powering a satellite is shown below. The array is connected to satellite by a thin aluminium rod. The array is facing the sun, and has a temperature of 1100 [K]1100\ \left[K\right], the satellite body has a temperature of15 K15\ K. Find the net heat transfer from the array to the satellite body.
The rod has a cross sectional area of 0.5 [m2]0.5\ \left[m^2\right].The square array and the satellite are facing one another and have 3 ×3 [m]3\ \times3\ \left[m\right]faces, they are 10 m10\ m apart.
kal=205 [WmK]k_{al}=205\ \left[\frac{W}{mK}\right]
Why are double pane windows more effective at preventing heat loss than single pane windows of the same thickness? Draw a diagram to demonstrate this property.
How much more effective are double pane windows are if kglass=1.05[WmK]k_{glass}=1.05\left[\frac{W}{mK}\right], kair=0.025[WmK]k_{air}=0.025\left[\frac{W}{mK}\right]. The single pane is 7 mm7\ mmthick, and the double panes are 3 mm3\ mmthick (air accounts for the remaining 1 mm1\ mm).
If we could vacuum pump the double pane window, what could happen to the heat flow through the window?
A square cooler contains drinks for a party at the beach. It contains the drinks and 1kg of ice and 2 kg of water. The cooler has side lengths of 50 cm50\ cm and is 5 cm5\ cm thick. The temperature during the day is 30°C30\degree C. The cooler is made of a layer of plastic that is 2.5 cm2.5\ cm thick and a 2.5 cm2.5\ cm thick layer of polyester. If the cooler got to the beach at 8 am how long would it take for all the ice to melt.
K values
Polystyrene: 0.033 wm⋅k\frac{w}{m\cdot k}
New Practice Question
Liquid helium is stored at its boiling point, 4.2 K, in a spherical capsule that is separated by a vacuum space from a surrounding container that is maintained at the temperature of liquid nitrogen, 77K. The capsule has a radius of 0.1 m and it is blackened on the outside. Calculate the amount of helium that boils away in one day. Now imagine the vacuum is replaced by a 20cm glass layer around the spherical capsule. How much helium boils away per day in this new condition?
LHe=20.9×103 JKgL_{He}=20.9\times10^3\ \frac{J}{Kg}
(kglass=1.05 wm⋅K)\left(k_{glass}=1.05\ \frac{w}{m\cdot K}\right)
A glass window pane has an area of 5.00 m2 and a thickness of 0.800 cm. If the temperature difference between its faces is 25.0°C, what is the rate of energy transfer by conduction through the window. (thermal conductivity of glass: kglass=0.8W/(m C))
Compound bar
A compound bar is made as shown below. It is insulated perfectly on its sides. If the cross-section of the bar is 5 cm25\ cm^2, what is the temperature at the junction of two metals and what is the total rate of heat flow? (kSt=50.2wm⋅K, kBr=109wm⋅K)(k_{St}=50.2 \frac{w}{m\cdot K},\ k_{Br}=109 \frac{w}{m\cdot K})