Heat, Temperature, and
Internal Energy
Starter
If a Fahrenheit thermometer registers a
10 degree temperature increase in air
temperature, what increase would a
Celsius thermometer register?
Note: DFo/DCo = 180/100
Why?
10/DC = 9/5
DC = 10(5/9) = 5.55
Internal Energy
E
• The total kinetic energy of all the molecules in the
substance.
• The units are Joules.
E = S KE
Example:
Answer:
A gas sample consists of 100 particles, each with a
kinetic energy of 2 Joules. What’s the internal energy?
E = 2 x 100 = 200Joules.
Temperature = Average KE
• Units depend of what scale you use
• T = E/N where N = # particles and E = internal
energy
Example:
A gas sample consists of 100 particles, each with
a kinetic energy of 2 Joules.
What’s the internal energy?
What’s the temperature?
Answer:
E = 2 x 100 = 200Joules.
T = E / 100 = 2 degrees.
Heat = energy transferred due to
a temperature difference
• Heat flows only from a warmer object to a cooler
one.
• Units are Joules or calories.
• Q is the symbol for heat.
A gas sample consists of 100 particles, each with a kinetic
energy of 2 Joules. If 300J of heat are added, what’s
the new temperature?
Answer:
E = 200J + 300J = 500J.
T = E / 100 =
5 degrees.
Note: the temperature increases if heat is added, as expected.
Heat Transfer Processes
Heat energy can be transferred from one body to another in three different
ways.
• Conduction: Energy is transferred when two objects are in direct
contact. Molecules of the hotter object bump into molecules of the
colder object and cause them to speed up, warming the colder object.
• Convection: Energy is transferred from one body to a cooler one via
currents in a fluid (a gas or liquid).
• Radiation: All objects, at any temperature, radiate electromagnetic
radiation (light of visible and invisible wavelengths). Unlike conduction &
convection, no medium (matter of any type) is necessary for heat transfer
through radiation. Objects absorb radiation as well. At thermal
equilibrium it will absorb as much as it radiates.
Sense of Touch
• Sensations of cold or hotness are not
reliable temperature readings.
• Sensations of cold or hotness tell you
about heat flow.
If you put one hand in hot water, the
other in cold, and then both in room
temperature water, each hand tells you
something different.
Which hand feels cool, and which feels
warm?
How is convection important in cooking?
Compare an iceberg to a cup of hot coffee.
a. Which has the greatest internal energy?
b. Which has the greatest temperature?
Temperature Scales
Fahrenheit: water freezes at 32 °F; boils at 212 °F
Celsius: water freezes at 0 °C; boils at 100 °C
So, DF / DC = 180 / 100 = 9/5 = 1.8
This means, a one degree step in Celsius is a 1.8
degree step in Fahrenheit.
OR, a one degree step in Fahrenheit, is a .56 step in
Celsius.
F = 32 + (9/5)C
C = 5/9 (F – 32)
There’s a problem with the
Celsius and Fahrenheit Scales,
and our definition of
temperature as Average KE.
What’s twice as hot as 40
degrees C?
What’s twice as hot as zero
degrees C?
What’s twice as hot as -10
degrees C?
Absolute Zero & the Kelvin Scale
The Kelvin scale is setup so that its zero point is the coldest possible
temperature--absolute zero, at which point a substance would have zero internal
energy. This is -273.15 °C, or -459.69 °F. Absolute zero can never be reached,
but there is no limit to how close we can get to it. Scientists have cooled
substances to within 10-5 Kelvin of absolute zero. How do we know how cold
absolute zero is, if nothing has ever been at that temperature? The answer is by
graphing Pressure vs. Temperature for a variety of gases and extrapolating.
P
A gas exerts no
pressure when at
absolute zero.
T (°C)
-273.15 °C
0 °C
Compare an iceberg to a cup of hot coffee.
a. Which has the greatest internal energy?
b. Which has the greatest temperature?
Calorie - the amount of heat that
will raise the temperature of 1
gram of water by 1 degree C.
1 calorie = 4.184 J
Systems of Units Used:
Calories and grams, Joules and
grams or Joules and kg.
When heat is added to a substance its temperature rises.
How much will it rise?
Q = heat added
DT = temperature change
M = mass of the substance
C = the specific heat of the substance
Q = mcDT
Some Specific Heats
Example
How much heat must be added to 500g of aluminum to
take it from 25 degrees Celsius to 125 degrees Celsius?
c = .215 cal / g oC
DT = Tf – Ti = 125 – 25 = 100 oC
m = 500g
Q = mcDT = 500(.215)(100) = 10750cal
Example
If 500cal of heat are added to 100g of lead at 25 degrees
Celsius, what will its final temperature be?
c = .031 cal / g oC
DT = Tf – Ti = Tf – 25
m = 100g
Q = mcDT ,
500 = 100(.031)(Tf – 25)
Tf = ((500)/(100)(.031)) + 25 = 161 + 25 = 186oC
If you mix two different substances
together and they reach a common final
temperature, then
Q 1 + Q2 = 0
Or
m1c1DT1 + m2c2DT2 =0
Example
A 100g piece of metal at 150 degrees C is
added to 500 grams of water at 20
degrees C. The metal and water end up at
30 degrees C. What was the specific
heat of the metal?
mwcwDTw+ mmcmDTm =0
500(1)(30 -20) + 100c(30-150) = 0
5000 – 12000c = 0 c = .416 cal/gC
When a pot of water is placed on the
stove, it heats and begins to boil at 100
degrees Celsius. As the water continues
to boil, the temperature
a. Slowly rises.
b. Stays the same.
c. Will drop slowly.
Latent Heat
The word “latent” comes from a Latin word that
means “to lie hidden.” When a substance changes
phases (liquid  solid or gas  liquid) energy is
transferred without a change in temperature. This
“hidden energy” is called latent heat.
Q = mcDT does not apply during a
phase change.
Latent Heat Formula
Q = m Lf or
Q = m Lv
Q = thermal energy
m = mass
L = heat of fusion or vaporization
Example:
Lf (the latent heat of fusion) for water is 80 cal/g.
Ice melts at 0ºC. 50 grams of ice at 0ºC will not become liquid until
additional heat is added. The amount of heat needed is:
Q = mLf = 50(80) = 4000 cal
In other words, it takes 4000 calories of heat to turn 40 grams of ice
at zero degrees C into 40 grams of water at zero degrees C.
Latent Heat For Water
Lf = 80 cal / g = 3.35 x 10 5 J/kg
Lv = 540 cal / g = 22.6 x 10 5 J/kg
Find the heat required to turn 100g of ice at -20
degrees C to 100 g of steam at 120 degrees C.
1st : Get the ice to its melting temp, 0 degrees C.
Q = mcDT = 100 ( .5) ( 0 – (-20)) = 1000 cals
2nd: Melt the ice
Q = mLf = 100(80) = 8000 cals
3rd:
Heat the
water to 100
GRAND
TOTAL
= degrees
Q = mcDT = 100 ( 1) ( 100 – 0 ) = 10000 cals
1000 + 8000+ 10000 + 54000 + 960
4th: Turn the water into steam
= 73960
Q = mLv =cal
100(540) = 54000 cals
5th: Heat the steam
Q = mcDT = 100 ( .48) ( 120 – 100) = 960 cals