Heat and
Temperature
A thermal infrared image of a ball before (left) and after (right)
being bounced.
DEFINITION OF HEAT
Heat is thermal energy that flows from a highertemperature object to a lower-temperature
object because of a difference in temperatures.
SI Unit of Heat:
joule (J) or calories (cal)
4.184 J = 1 cal
4184 J = 1 Cal = 1 kcal
What is the difference between a hot cup of coffee and a cold
cup of water?
In a hot cup of coffee there is more activity – the atoms are
jiggling around more. We say that they have more kinetic
energy. We might even say that they have more thermal energy
(energy of random motion) or more internal energy because more
energy is internal to the system.
Which has more internal energy, a cup of hot water or an iceberg?
The iceberg because it has more molecules jiggling
The heat that flows from hot to cold
originates in the internal energy of
the hot substance.
It is not correct to say that a substance
contains heat.
Internal energy is the total energy that
the molecules possess (kinetic plus
potential).
Kinetic energy can be translational and
rotational. Molecules have potential energy
because of intermolecular forces.
When we heat a substance, we increase
Its internal energy.
Temperature is related to the internal energy
per molecule or the average kinetic energy
of translational motion of molecules.
Why do we give sparklers that burn at 12000C to kids ?
There are not many
combustible molecules in the
sparkler so not much total
energy – certainly below the
kids threshold of feeling…so
Although the temperature is
high, (the amount of internal
energy per molecule), the total
internal energy is low!
Measuring Temperature
Thermometers use liquids that expand or contract easily with
temperature. The liquid absorbs or transfers thermal energy.
We say that a thermometer “measures its own temperature”…
because any two things put together will come to the same
temperature.
When this happens, the thermometer and its environment are
said to be in thermal equilibrium.
A poorly constructed thermometer thus has the ability to change
the temperature of its surroundings by absorbing too much heat.
Scales of Temperature
Temperatures are reported in degrees
Celsius, degrees Fahrenheit or
degrees Kelvin.
0 K is the temperature at which an ideal
gas can theoretically be compressed to
zero volume (called absolute zero)
Kelvin temperatures are always positive
so can be related proportionally to the
average kinetic energy per molecule
KEAv = 3/2 kT
Scale Conversions
There are 180 divisions on the 0F scale
compared with 100 divisions on the oC
scale so the scale factor is…..
180 / 100 = 9 / 5
because the 0F scale begins at 32 rather
than 0 we must add this on, so…..
TF = (9/5 TC) + 32.0
For the Kelvin scale, the freezing point of
water is 273.15 K above absolute zero so..
TK = TC + 273.15
Temperature Practice
1. Normal body temperature is 98.6 0F. What is this on the Centigrade scale?
TC = 5/9 (TF – 32) = 5/9 (98.6 – 32) = 370C
2. Room temperature is often taken to be 680F. What is this on the Centigrade
and Kelvin scales?
TC = 5/9 (TF – 32) = 5/9 (68 – 32) = 200C
TK = TC + 273.15 = 20 + 273.15 = 293.15 K
3. The temperature of a filament in a light bulb is about 18000C. What is
this on the Fahrenheit and Kelvin scales?
TC = (9/5 TC ) + 32 = (9/5 1800) + 32)
= 32720F
TK = TC + 273.15 = 1800 + 273.15 = 2073 K
Processes of Thermal Energy Transfer
Conduction
Conduction is the process by which kinetic energy is passed from
molecule to molecule
Metals have a lot of loose (free)
electrons which can transmit
vibrations (KE) quickly when high
speed particles collide with slower
moving ones. We say they are
good heat conductors.
All gasses (and most liquids) tend to be poor conductors. We say
that they are good thermal insulators.
Conduction Examples
• Wooden or rubber handles on frying pans
• Clothing worn in layers to trap air – a poor conductor
• Wood or tiled floor feels cooler than carpet even though they
are at the same temperature
• Wood or tiled floor feels cooler than carpet even though they
are at the same temperature
• Snowflakes trap air in their crystals so are good insulators.
Snow slows the escape of heat from the earth’s surface, so
good for Eskimo dwellings and protection for animals from the
cold.
Processes of Thermal Energy Transfer
Convection
In convection, thermal energy moves between two points because
of a bulk movement of matter
When part of a fluid is heated, it tends to expand and thus its
density is reduced. The colder fluid sinks and the hotter fluid rises
up.
This thermal infrared image shows hot oil
boiling in a pan. The oil is transferring
heat out of the pan by convection. Notice
the hot (yellow) centers of rising hot oil
and the cooler outlines of the sinking oil.
Convection Examples
• Central heating causes a room to warm
up because a convection current is set
up. The heat source should be near the
ground.
• Pilots of gliders (and many birds) use naturally occurring
convection currents to stay above the ground
• Sea breezes (winds) are often due to convection. During the
day the land is hotter than the sea. Hot air rises from the land
and there is a breeze onto the shore. During the night the
situation is reversed.
• A refrigerator cooling coil is placed at the top of the unit so that
colder air sinks downwards and the warmer air is displaced
upwards and cooled by the coil thus establishing a convection
current.
Processes of Thermal Energy Transfer
Radiation
Radiation is the process in which energy is transferred by means
of electromagnetic waves.
For most everyday objects, this radiation is in the infra-red part of
the electromagnetic spectrum.
The source of EM waves is vibrating electrons in matter
A thermal infrared image of the center of our
galaxy. This heat from numerous stars and
interstellar clouds traveled about 24,000 light
years (about 150,000,000,000,000,000
miles!) through space by radiation to reach
the infrared telescope
Points to note:
• An object at constant temperature will both absorb and radiate
energy at the same rate.
• A surface that is a good radiator is also a good absorber.
• Surfaces that are light in color and smooth (shiny) are poor
radiators (and poor absorbers). The reverse is true for dark and
rough surfaces.
• If the temperature of an object is increased then the frequency
of the radiation increases. The total rate at which the energy is
radiated will also increase.
• Radiation can travel through a vacuum
(space)
Radiation Examples
• The sun warms the Earth’s surface by radiation (principally
short wavelength/high frequency IR)
• The earth re-radiates energy back as low frequency radiation
because the earth’s temperature is so low. The atmosphere is
transparent to visible (high f) light but longer wavelengths are
absorbed and reradiated back to earth especially by excess
carbon dioxide and water vapor leading to increased global
warming.
• People wear light colored clothing in summer as it tends to not
absorb the radiation from the sun.
• A Halogen cook top uses several quartz-iodine lamps
underneath a ceramic top (low conductivity). The EM radiation
passes through the ceramic top and is absorbed by the bottom
of the pot.
• Thermos flask has silvered inside surface to reduce radiation.
Heat and Specific Heat
A person puts a pan on a stove heating ring and returns a few
seconds later to find that the pan is hot. The same person puts a
pan of water on the stove ring and returns minutes later to find that
the pan is warm but far from hot. What does this tell you?
Some substances will absorb a lot of heat for only a small change
in temperature.
Iron with a little heat will shoot up in temperature while water takes
a lot of heat energy to make the temperature higher.
Why is this?
Heat and Specific Heat
Temperature has a lot to do with the translational back and forth
motion of atoms or molecules
Iron’s electrons move rapidly back and forth and the temperature
goes up quickly
But…water doesn’t just shake back and forth, the molecules
pucker in and out storing the energy in internal rotational states
(potential energy) and the hydrogen bonding sticks them together
so they don’t shake as much, so the temperature is not driven up
as much.
We say that water stores an enormous capacity of heat for small
temperature changes – This is called specific heat
Heat and Specific Heat
We can define the heat capacity, C, of an object as the energy
required to raise its temperature by 1 K. This is different for
different substances.
C = Q / T
units: J / K or J / 0C
Specific heat capacity, c, is the energy required to raise a unit
mass of a substance by 1 K.
c = Q / (m T)
units: J / kg K or J / kg 0C
We say that water stores an enormous capacity of heat for small
temperature changes – This is called specific heat
Heat and Temperature Change: Specific Heat Capacity
Heat and Specific Heat
It turns out that water will absorb a whole calorie of heat energy
per gram and only change temperature by 1 degree Celcius
(centigrade)
We can think of specific heat as “thermal inertia” because it
signifies the resistance of a substance to a change in
temperature.
Q = m c t
c = specific heat capacity (cal/g0C)
m = mass of object
cwater = 1 cal/g0C
or
4.184 J/g0C
or
4184 J/kg0C
t = change in
temperature
Heat and Specific Heat
How much energy does it take to raise the temperature of 1.5 liters of
water by 200C?
mwater = 1.5 L ( 1kg / 1L) = 1.5 kg
T = 20oC
cwater = 1000 cal/kg0C or 4184 J/kg0C
Q = m c t
Q = (1.5 kg) (1000 cal/kg0C) (200C)
= 30 000 cal
Q = (1.5 kg) (4184 J/kg0C) (200C)
= 125 520 J = 130 000 J
Heat and Specific Heat
Some high temperature foods, you can eat comfortably when you take
them out of the oven as they have a low specific heat capacity and
therefore don’t hold much thermal energy but water filled foods like pie
filling you can burn your mouth on as the high temperature food will hold a
lot of energy.
A hot water bottle contains boiling water that cools gradually during the
night releasing a large amount of thermal energy.
Countries surrounded by water (which has a high specific heat) are heated by
the warm winds that have absorbed thermal energy from the ocean (cons of
energy). The ocean cools gradually during the winter so maintains a constant
source of heat energy. The water acts as a temperature moderator, absorbing
energy from the air above in the summer and releasing it in the winter.
Heat and Temperature Change: Specific Heat Capacity
A Hot Jogger
In a half-hour, a 65-kg jogger can generate 8.0x105J of heat. This heat
is removed from the body by a variety of means, including the body’s own
temperature-regulating mechanisms. If the heat were not removed, how
much would the body temperature increase?
Q  m cT
5
8.0

10
J
Q
 3.5 C
T 

mc
 65 kg  3500 J kg  C 


Heat and Temperature Change: Specific Heat Capacity
CALORIMETRY
If there is no heat loss to the surroundings,
the heat lost by the hotter object equals the
heat gained by the cooler ones.
Heat and Temperature Change: Specific Heat Capacity
Measuring the Specific Heat Capacity
The calorimeter is made of 0.15 kg of aluminum
and contains 0.20 kg of water. Initially, the
water and cup have the same temperature
of 18.0oC. A 0.040 kg mass of unknown
material is heated to a temperature of
97.0oC and then added to the water.
After thermal equilibrium is reached, the
temperature of the water, the cup, and the
material is 22.0oC. Ignoring the small amount
of heat gained by the thermometer, find
the specific heat capacity of the
unknown material.
Heat and Temperature Change: Specific Heat Capacity
mcT Al  mcT water  mcT unknown
 mcT Al   mcT water
cunknown 
 mT unknown








9.00 102 J kg  C   0.15 kg  4.0 C   4186 J kg  C   0.20 kg  4.0 C




 0.040 kg  75.0 C

 1300 J kg  C



Phase Changes
Why do you feel cold when you get out of a pool and a breeze
is blowing?
Water evaporates off your body and cools you down. How come?
Why is evaporation a cooling process?
Molecules in a liquid have a distribution of speeds and the average
relates to what we call Temperature. When faster moving
molecules leave a liquid’s surface they leave behind the slower
moving molecules, which lowers the average speed and therefore
the temperature of the liquid.
Normal
distribution curves
of molecular
speeds for ideal
gas at 100 K and
900 K respectively
Phase Changes
In hot climates, sacking is put over clay pots and kept wet. Why?
Evaporation of water from the sack cools the sack and thus draws thermal
energy outwards from the water inside the pot. This keeps the drinking
water nice and cool.
How do we keep cool?
We perspire (sweat), so evaporation takes place from our skin’s surface.
Why do dogs pant? (or other animals without sweat glands)
They can’t sweat so they create a large surface area (tongue and
bronchial tract) from which liquid can evaporate and therefore cool
them down.
Similarly rubbing your hands under a hand dryer creates a larger
surface for water to evaporate.
Phase Changes
Evaporation depends upon the temperature of the liquid and air
surrounding the liquid, the surface area of the liquid and the moisture
content in the air (humidity). Evaporating molecules form a vapor above
the liquid. Equilibrium is reached when the vapor pressure exerted on the
fluids surface returns liquid molecules to the liquid at the same rate they
leave.
How do fans keep people cool?
Lower vapor pressure so more evaporation so….more cooling
Why are their warning signs on hot tubs about staying in too
long?
In a hot tub you sweat like mad but the water can’t evaporate off the
skin so your body heats up and can be dangerous if you stay in too
long.
Name at least two ways to cool a hot cup of coffee?
Increase evaporation by blowing on it, pouring it into a saucer
Cool by conduction by pouring in cool saucer, adding ice cubes,
stirring with cool silverware
Phase Changes
Is condensation a heating or a cooling process?
It is a heating process. The slower moving water vapor molecules stick
together (forming droplets) while the higher speed molecules remain in the
gaseous state thus increasing the average KE of the air molecules and thus
the temperature.
Why do people dry off in a steamy bathroom?
The cooling effect of water evaporating off their body is balanced by
the heating effect of steam condensing on it. That is why my 4-year old
daughter asks for the warm water to be left in the tub while she is
drying off.
Phase Changes
If evaporation is a cooling process is boiling a heating process?
Heating the water in a pan is a heating process but the act of boiling is
actually a cooling process. Like evaporation, when boiling, molecules leave
the surface of the liquid taking thermal energy with them.
What influences the ability of a liquid to boil other than temperature?
The air pressure acting on the liquid
Heat pan of water, bubbles form but 30km of air pushing down
(atmospheric pressure) squashes these bubbles. With more heating
the temp keeps increasing and the molecules become more energetic
until bubbles are able to withstand the pressure. This temps for water
is 1000C at sea level.
What happens to this process if you are up a mountain?
Closer to top of air therefore less pressure so bubbles stay
formed at a lower temperature.
Phase Changes
You normally cook eggs for 3 minutes at sea level. Do you cook
them for a longer or shorter time when living at higher altitude?
Longer as water boils at a lower temp
If you heat water at atmospheric pressure it boils at 1000C but if you
turn up the heat it doesn’t get any hotter, how come?
The more you heat, the more vigorous the boiling but you also have
more liquid escaping therefore more cooling so they offset each other.
(you can also think of it as the heat input going towards breaking
intermolecular bonds and not towards changing the average kinetic
energy of the molecules).
If you put a cover on a pan of spaghetti will it cook faster?
Yes, the lid increases the pressure so temp goes up more before
bubbles stay formed.
Phase Changes
Why are sensitive fruit crops in the South sprayed with water before
a forecasted frost?
Like condensation (gas to liquid), changing state from liquid to solid is
also a heating process. The heat liberated in freezing the layer of
water around the outside of the strawberry, actually protects the
strawberry inside.
Phase Changes
In the past, farmers used to put a tub of water in the cellar where
they stored their canned food. Why?
If the temperature in the cellar dropped the water in the tub would
freeze before the liquid in the cans (which had added salt or sugars)
thus releasing heat and warming the room.
Phase Changes
Which will hurt more, a steam burn at 1000C or a water burn at
1000C ?
The steam burn is much more serious because each gram of steam
liberates 540 calories when it condenses, whereas water only liberates
1cal for every gram for every degree (or only 100 cal to go from 1000C
to 0 0C).
Note: When 540 cal is used to turn a gram of water into steam it does not
go into increasing the molecules KE, so it must go into increasing their PE.
Intermolecular bonds have to be broken and this takes a lot of energy.
When steam condenses, bonds form and this energy is released.
Phase Changes
Why is an ice rink flooded with hot water to smooth out the ice?
Wouldn’t cold water work better?
Above 800C, hot water freezes faster than warm water. For a large
surface area like an ice skating rink, the rate of cooling by rapid
evaporation is very high because each gram of water that evaporates,
draws at least 540 cals/gram from the water left behind.
This is huge compared with the 1 cal/g/0C that is drawn for each gram
of water that cools by thermal conduction.
Phase Changes
Latent Heat of Fusion:
The quantity of heat needed per kg to melt a solid (or solidify a liquid)
at constant temperature and atmospheric pressure.
Change in heat = (mass)(heat of fusion)
Q = m Lf
Lf units: J/kg
Lf,water = 80 cal/g or 3.35 x 105 J/kg
Latent Heat of Vaporization:
The quantity of heat needed per kg to vaporize a liquid (or liquefy a
gas) at room temperature and atmospheric pressure.
Change in heat = (mass)(heat of vaporization)
Q = m Lv
Lv units: J/kg
Lv,water = 540 cal/g or 2.26 x 106 J/kg
More than 6x’s Lf for water
Phase Changes
Latent Heat of Fusion:
The quantity of heat needed per kg to melt a solid (or solidify a liquid)
at constant temperature and atmospheric pressure.
Change in heat = (mass)(heat of fusion)
Q = m Lf
Lf units: J/kg
Lf,water = 80 cal/g or 3.35 x 105 J/kg
Latent Heat of Vaporization:
The quantity of heat needed per kg to vaporize a liquid (or liquefy a
gas) at room temperature and atmospheric pressure.
Change in heat = (mass)(heat of vaporization)
Q = m Lv
Lv units: J/kg
Lv,water = 540 cal/g or 2.26 x 106 J/kg
More than 6x’s Lf for water
Gas Laws
Atmospheric Pressure
The earth’s atmosphere has density therefore it has weight.
At sea level (200C) it has a density of 1.2 kg/m3
The weight of 30km of air on each square meter at the earth’s
surface is about 100 000 N (105 N).
A Pascal is 1 N/m2 so the pressure is reported as 100 000 Pa or 100
kPa. It is actually 101.3 kPa.
Barometers and pumps rely on the atmospheric pressure to push a
liquid up an evacuated tube.
The pressure at the bottom of a mercury barometer must be the same
as the atmospheric pressure (otherwise liquid would keep on being
pushed up the tube).
Similarly, a vacuum pump can only raise water up a height of 10.3m as
mercury is pushed up 76 cm and is 13.6 times more dense as water
(13.6 x 0.76m = 10.3m)
Gas Laws
Robert Boyle (1627-1691)
The volume of a gas is inversely proportional to the pressure applied
when the temperature is kept constant.
V  1/ P (constant T)
PV = constant
P1V1 = P2V2
Kinetic Theory Interpretation
The pressure exerted on the wall of a container is due to the constant
bombardment of molecules. If the volume is reduced (say in half), the
molecules are closer together and twice as many will be striking a
given area of the wall per second, hence the pressure will be twice as
great.
Gas Laws
Archimedes Principle (Buoyancy)
Buoyant forces are caused by a difference in pressure on the top and
bottom surfaces of a submerged object.
The buoyant force on a body immersed in a fluid is equal to the weight
of the fluid displaced by the object.
FB = F g V
(for submerged portion of the object placed in the fluid)
Any object that has a mass less than the mass of an equal volume of
the surrounding fluid (air or liquid) will rise.
In other words for air if any object is less dense than the surrounding
air around it, it will rise. Heating air in a hot air balloon has this effect.
Gas Laws
Examples
1. To capture its prey a whale will create a cylindrical wall of bubbles
beneath the surface of the water, trapping the confused fish inside. If
an air bubble has a volume of 5.0 cm3 at a depth where the water
pressure is 2.00 x 105 Pa, what is the volume of the bubble just before
it breaks the surface of the water?
P1 = 2.00 x 105 Pa
V2 = P1V1 / P2
V2 = 9.90 cm3
V1 = 5.00 cm3 P2 = 1.01 x 105 Pa V2 = ?
= (2.00 x 105 Pa)(5.00 cm3) / (1.01 x 105 Pa)
Gas Laws
Examples
2. In a jet liner ascending from sea level where the cabin pressure starts off
at 1.01 x 105 Pa to flying altitude where the cabin pressure drops slightly to
1.00 x 105 Pa despite pressurized conditions. A person will feel a strange
sensation in their middle ear, whose volume is 6.0 x 10-7 m3. What is the
new volume of air inside the person’s middle ear and what can they do to
compensate for this change in volume?
P1 = 1.01 x 105 Pa
V1 = 6.0 x 10-7 m3
P2 = 1.00 x 105 Pa
V2 = ?
P1V / T1 = P2V / T2
V2 = P1 V1 / P2
= (1.01) (6.0 x 10-7 m3) / (1.00)
= 6.1 x 10-7 m3
Swallowing or yawning clears the Eustachian tube by reducing the volume
of air.
Gas Laws
Examples
3. Mr. Fawcett is diving at a dept of 20m off the coast of Mexico where the
density of water is 1025 kg/m3 and the pressure is 3.06 x 105 Pa. If he
foolishly hold s his breath as he ascends to the surface, how many times
would the volume of his lungs change (assuming the water temp stays
constant)? Would his lungs be crushed or would they expand? What is
the best way to ascend after diving?
P1 = 3.06 x 105 Pa
P2 = 1.01 x 105 Pa
V2 / V1 = ?
V2 / V1 = P1 / P2 = (3.06 x 105 Pa) / (1.01 x 105 Pa) = 3.03 times bigger
His lungs would blow up like a balloon
He could continue releasing air from his lungs while ascending
* Note pressure with depth is calculated using:
P = gh + atmos pressure
P = (1025 kg/m3)(10 N/kg)(20m) + 101.3 x 103 N/m2
P = 3.06 x 105 N/m2 (Pa)
Gas Laws
Examples
4. A 5450 m3 blimp circles Fenway Park during the Word Series, suspended
in earth’s 1.21 kg/m3 atmosphere. The density of the helium in the blimp
is 0.178 kg/m3.
a) What is the buoyant force that suspends the blimp in the air?
b) How does this force compare to the blimp’s weight?
c) How much weight in addition to helium, can the blimp carry and still
continue to maintain a constant altitude?
F = 1.21 kg/m3 V = 5450 m3 g = 10 N/kg
H = 0.178 kg/m3
a) FB = F g V = (1.21 kg/m3) (10 N/kg) (5450 m3) = 65 945 N = 65 900 N
b) The blimp is suspended so it is the same
c) Weight of Helium = H g V = (0.178 Kg/m3)(10 N/kg)(5450 m3) = 9701 N
Therefore weight that can be added is 65 945 N – 9701 N = 56 200N
Gas Laws
Examples
5. Floating on her back in the beautiful Caribbean during her spring break a
student has a density of 980 kg/m3 and a volume of 0.060 m3. What
buoyant force supports her in the sea, which has a density of 1025
kg/m3?
F = 1025 kg/m3
s = 980 kg/m3
g = 10 N/kg
V = 0.060 m3
FB = Wt = s g V = (980 kg/m3) (10 N/kg) (0.060 m3) = 588N = 590N
Note: Buoyant force can’t be more than her weight because she is
floating. She is not submerged as he density is less than that of
sea water.
Gas Laws
Examples
6. Swimming in her backyard pool, a student attempts to hold a 0.9000 m3
inner tube under the water. If submerged what buoyant force will be
exerted? If the tube is then let go and pops up with a force of 8990N,
what is the weight of the inner tube?
F = 1000 kg/m3
g = 10 N/kg
V = 0.9000 m3
FB = F g V = (1000 kg/m3) (10 N/kg) (0.9000 m3)
Wt = FB – F
= 9000N – 8990N
= 10N
= 9000 N