Heat Loss mechanisms
Aims
 To understand the different mechanisms of heat transfer.
 To carry out an experiment demonstrating some of these mechanisms and the
properties of different coloured surfaces.
Part 1: Tutorial question (15mins)
1.1
What are the three mechanisms of heat transfer?
1.2
Here are two equations used that describe different types of heat transfer:
H
kAT
l
[1]
H  A .T 4
[2]
State which mechanisms equations 1 and 2 belong to, and, describe what each
of the symbols represent giving their standard units.
 Three identical metal bottles are placed on an insulated surface and differ only by
surface colour; one is black, one is white, and one is silver. They are each filled
with the same volume of boiling water and allowed to cool.
1.3
Which mechanisms of heat transfer will be significant?
1.4
Which bottle will cool quickest and why? Which bottle will cool
slowest and why?

Part 2: Monitoring water cool in different containers (25mins)
Warning: this experiment uses boiling water. Please take care when handling
boiling water to avoid scalding yourself or your lab partner. Also, please use the
insulated gloves provided when filling metal bottles or moving them around.
The apparatus should be set up as follows:
bottles
timer
thermometers
kettle
Figure 1
 Firstly, pour at least 1 litre of water in the kettle and switch the kettle on to boil.
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 Use the plastic measuring jug provided to pour some of the boiling water into each
of the three metal bottles to heat them up - funnels are provided to ease the pouring
and minimise spillages.
 Pour all the water from the bottles back into the kettle and switch it on to boil
again.
You will now fill each bottle with 300ml of boiling water but it is important the
starting temperatures of are the same – differing by no more than 2 °C. The following
procedure should ensure this for you, if not ask a demonstrator.
 You should now use the measuring jug and funnel to pour 300ml of boiling water
into the silver bottle, then pour 150ml of boiling water into the white bottle, next
pour 300ml of water into the black bottle and the final 150ml into the white bottle
again.
 Place a digital thermometer into each of the bottles and seal with caps to reduce
heat loss by convection.
 Start the timer and note the temperatures of the black, white and silver bottles –
check that their temperatures are all within 2 °C of each other.
 Take temperature measurements of each bottle every minute for a total of 20
minutes. These readings should be to the accuracy of the thermometer i.e. one
decimal place.
Part 2: Analysis (10 mins)
2.1
Plot a graph of the cooling for all three bottles on the one graph. Draw a line
(curve) of best fit through each set of points. (Please use different symbols
and/or colours to distinguish between the three different bottles).
2.2
Which bottle cooled the slowest? Give an explanation for your answer.
Which bottle cooled the fastest? Is this related to the properties of the colour
of the bottle or because the starting temperature differed slightly from the rest?
2.3
What is the dominant heat loss process for the bottles?
Part 3: (Optional)
Take a look at the Crookes Radiometer and observe what happens when light is
incident upon one side.
3.1
Can you explain the movement of the “paddles” contained within the vacuum?
Hint:
One side of the paddle is black and the other is white.
Further work
The following questions will help in understanding the topic covered by this
experimental tutorial.
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Mastering Physics: Thermal 2: Heat Transfer. There are two questions on “Radiation
of Heat” concerned with “Understanding Heat Radiation” and “Heat Radiated by a
Person”.
Demonstrators' Answers, Hints, Marking Scheme and Equipment List
Marking Scheme
Section
1.1
1.2
1.3
1.4
2.1
2.2
2.3
Discretionary mark
TOTAL
Mark
1
1
1
1
2
1
1
2
10
Answers
1.1
Conduction – transfer of heat through a material by transfer of energy from
one atom/molecule to its neighbours by a variety of mechanisms (e.g. through
lattice vibrations in a solid, movement of conduction electrons in a conductor,
exchange of energy via molecular collisions in gases / liquids)
Convection – transfer of heat by movement of material, only applies to fluids
such as gases and liquids.
To model this we need to understand density changes on heating as well as
fluid dynamics – not easy to write equations!
Radiation – transfer of heat by the emission of electromagnetic radiation –
occurs from all objects at all temperatures, but radiated power and wavelength
distribution depends on T.
1.2
Conduction [1]
H = k A T / l
H is heat transferred per second (W)
k is the thermal conductivity (W m-1 K-1)
T is temperature difference (K)
A is the area across which the heat is transferred (m2)
l is the length over which the heat is transferred (m)
Radiation [2]
H = A T4
H is heat transferred per second (W)
A is the surface area of the object (m2)
 is the emissivity (varies from 0 – 1)
 is Stefan’s constant (W m-2 K-4)
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T is the absolute temperature in K
1.3
Conduction should be insignificant, due to the low thermal conductivity of air,
and the insulated surface. So convection and radiation will play the biggest
part.
1.4/1.5 Basically use these two questions to promote a discussion and then prompt
students to test their theories by doing the experiment without giving an
answer to these latter two questions.
2.1
should see a similar trend to the graph below.
90
88
86
84
82
black
80
silver
78
white
76
74
72
70
0
2
4
6
8
10
2.2
The silver bottle should cool slowest. Silvered surfaces have very low
emissivity and so lose relatively little to radiation.
2.3
Accept any reasonable, well explained answer.
The black bottle should cool fastest. Black has the highest emissivity, e, of ~1
and so loses the most to radiation.
However, emissivities of different paints and coatings, whilst varying widely
at optical wavelengths are mostly similar at infrared wavelengths.
The peak of the blackbody spectrum at 90 °C = 363 K is at a wavelength of
about 8 microns, much longer than optical wavelengths of about 0.3-0.7
microns.
For 8 microns wavelength, we would expect emissivity values in the range of
about 0.8-0.9 for common anodized aluminium coatings, along with many
other paints.
Plain aluminium at this wavelength has an emissivity of about 0.03. So a clear
difference between aluminium and the paints should be seen, however
detecting differences between the black and white coatings will be difficult if
at all possible.
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2.4
The dominant heat loss process for the bottles is convection – the differences
in radiative losses due to differences in emissivity were small relative to the
overall cooling rate, the overall cooling rate must therefore have been
dominated by the other main process – convection.
3. Crooke’s Radiometer.
Not as straightforward as you might first think – note it rotates the wrong way for it
being radiation pressure !
The following is from Wikipedia.
Over the years, there have been many attempts to explain how a Crookes radiometer
works:
1. Crookes incorrectly suggested that the force was due to the pressure of light. This
theory was originally supported by James Clerk Maxwell who had predicted this
force. This explanation is still often seen in leaflets packaged with the device. The
first experiment to disprove this theory was done by Arthur Schuster in 1876, who
observed that there was a force on the glass bulb of the Crookes radiometer that was
in the opposite direction to the rotation of the vanes. This showed that the force
turning the vanes was generated inside the radiometer. If light pressure was the cause
of the rotation, then the better the vacuum in the bulb, the less air resistance to
movement, and the faster the vanes should spin. In 1901, with a better vacuum pump,
Pyotr Lebedev showed that in fact, the radiometer only works when there is low
pressure gas in the bulb, and the vanes stay motionless in a hard vacuum. Finally, if
light pressure were the motive force, the radiometer would spin in the opposite
direction as the photons on the shiny side being reflected would deposit more
momentum than on the black side where the photons are absorbed. The actual
pressure exerted by light is far too small to move these vanes but can be measured
with devices such as the Nichols radiometer.
2. Another incorrect theory was that the heat on the dark side was causing the material
to outgas, which pushed the radiometer around. This was effectively disproved by
both Schuster's and Lebedev's experiments.
3. A partial explanation is that gas molecules hitting the warmer side of the vane will
pick up some of the heat i.e. will bounce off the vane with increased speed. Giving the
molecule this extra boost effectively means that a minute pressure is exerted on the
vane. The imbalance of this effect between the warmer black side and the cooler
silver side means the net pressure on the vane is equivalent to a push on the black
side, and as a result the vanes spin round with the black side trailing. The problem
with this idea is that the faster moving molecules produce more force, they also do a
better job of stopping other molecules from reaching the vane, so the force on the
vane should be exactly the same — the greater temperature causes a decrease in local
density which results in the same force on both sides. Years after this explanation was
dismissed, Albert Einstein showed that the two pressures do not cancel out exactly at
the edges of the vanes because of the temperature difference there. The force
predicted by Einstein would be enough to move the vanes, but not fast enough.
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4. The final piece of the puzzle, thermal transpiration, was theorized by Osborne
Reynolds, but first published by James Clerk Maxwell in the last paper before his
death in 1879. Reynolds found that if a porous plate is kept hotter on one side than the
other, the interactions between gas molecules and the plates are such that gas will
flow through from the cooler to the hotter side. The vanes of a typical Crookes
radiometer are not porous, but the space past their edges behave like the pores in
Reynolds's plate. On average, the gas molecules move from the cold side toward the
hot side whenever the pressure ratio is less than the square root of the (absolute)
temperature ratio. The pressure difference causes the vane to move cold (white) side
forward.
Both Einstein's and Reynolds's forces appear to cause a Crookes radiometer to rotate,
although it still isn't clear which one is stronger.
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Equipment List:
3 x bottles (black, white, silver)
3 x thermometers
Kettle
Timer
Foil
Bottle rack
3 x different coloured pencils
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