Lecture 23
Specific Heat and Phase Changes
Today’s Topics:
• Heat and Temperature Change
– Specific heat
• Heat and Phase Change
– Latent heat
Heat and Temperature Change
Heat is energy that flows from a higher-temperature object to a lowertemperature object because of a difference in temperatures.
SI Unit of Heat: joule (J)
The heat that must be supplied or removed to
change the temperature of a substance is
Q = mcDT
specific heat
capacity
SI Unit for Specific
Heat Capacity: J/(kg·K)
OTHER ENERGY UNITS
1 kcal = 4186 joules
1 cal = 4.186 joules
ACT: Thermal Contact
Two objects are made of
the same material, but have
different masses and
temperatures. If the
objects are brought into
thermal contact, which
one will have the greater
temperature change?
a) the one with the higher initial temperature
b) the one with the lower initial temperature
c) the one with the greater mass
d) the one with the smaller mass
e) the one with the higher specific heat
Because the objects are made of the same material, the only
difference between them is their mass. The object with less mass
will change temperature more easily because not much material is
there (compared to the more massive object).
ACT: Two Liquids
The same amount of heat is added to two
equal-mass liquids, that are initially at the
a) the cooler one
same temperature. You measure the
b) the hotter one
temperatures and find that one liquid has a
higher temperature than the other. Which
c) both the same
liquid has a higher specific heat?
Both liquids had the same increase in internal energy,
because the same heat was added. But the cooler liquid
had a smaller temperature change.
Because Q = mc∆T, if Q and m are both the same and ∆T
is smaller, then c (specific heat) must be bigger.
ACT: Night on the Field
The specific heat of concrete is
greater than that of soil. A baseball
field (with real soil) and the
surrounding parking lot are warmed
up during a sunny day. Which would
you expect to cool off faster in the
evening when the sun goes down?
a) the concrete parking lot
b) the baseball field
c) both cool off equally fast
The baseball field, with the lower specific heat, will change
temperature more readily, so it will cool off faster. The high specific
heat of concrete allows it to “retain heat” better and so it will not cool
off so quickly—it has a higher “thermal inertia.”
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.
Calorimetry
a) 0°C
1 kg of water at 100°C is poured into a
b) 20°C
bucket that contains 4 kg of water at 0°C.
c) 50°C
Find the equilibrium temperature (neglect
d) 80°C
the influence of the bucket).
e) 100°C
Because the cold water mass is greater, it will
have a smaller temperature change!
The masses of cold/hot have a ratio of 4:1, so
the temperature change must have a ratio of
1:4 (cold/hot).
Q1 = -Q2
m1cΔT1 = -m2cΔT2
| ΔT1 /ΔT2 | = m2 / m1
Example: Heat and Temperature
Two spheres, labeled A and B, have identical masses, but are made of different
substances. The specific heat capacity of sphere A is cA = 440 J/(kg ∙ oC) and
that of sphere B is cB = 160 J/(kg ∙ oC). The spheres are initially at 21 oC; and the
same quantity of heat is added to each sphere. If the final temperature of sphere
A is 72 oC, what is the final temperature of sphere B?
Example
A 0.20-kg lead ball is heated to 90.0 oC and dropped into an ideal calorimeter
containing 0.50 kg of water initially at 20.0 oC. What is the final equilibrium
temperature of the lead ball? The specific heat capacity of lead is 128 J/(kg ∙ oC);
and the specific heat of water is 4186 J/(kg ∙ oC).
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 18.0 oC. A 0.040 kg mass
of unknown material is heated to a temperature of 97.0 oC and then added to the
water. After thermal equilibrium is reached, the temperature of the water, the cup,
and the material is 22.0 oC. Ignoring the small amount of heat gained by the
thermometer, find the specific heat capacity of the unknown material.
cunknown =
[
9.00 ´10 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 )
2
cunknown
(mcDT )Al + (mcDT )water
(mDT )unknown
!
!
!
!
(
cunknown = 1300 J kg × C!
)
!
Heat and Phase Changes
THE PHASES OF MATTER
During a phase change, the temperature of
the mixture does not change (provided the
system is in thermal equilibrium).
Latent Heat
The heat that must be supplied or removed to change the
phase of a mass m of a substance is
SI Units of Latent Heat: J/kg
latent heat
Solving problems involving phase changes is
similar to solving problems involving heat
transfer, except that the latent heat must be
included as well.
Example
A thermos bottle contains 3.0 kg of water and 2.0 kg of ice in thermal equilibrium at
0 oC. How much heat is required to bring the system to thermal equilibrium at 50 oC?
ACT: Adding Heat
If you add some heat to a substance,
is it possible for the temperature of
the substance to remain unchanged?
a) yes
b) no
Yes, it is indeed possible for the temperature to stay the same. This is
precisely what occurs during a phase change—the added heat goes
into changing the state of the substance (from solid to liquid or from
liquid to gas) and does not go into changing the temperature! Once
the phase change has been accomplished, then the temperature of the
substance will rise with more added heat.
ACT: Hot Potato
Will potatoes cook faster if the
water is boiling faster?
a) yes
b) no
The water boils at 100°C and remains at that temperature until all
of the water has been changed into steam. Only then will the
steam increase in temperature. Because the water stays at the
same temperature, regardless of how fast it is boiling, the
potatoes will not cook any faster.
ACT: Spring Break
You step out of a swimming
pool on a hot day, where the
air temperature is 90°F.
Where will you feel cooler, in
Phoenix (dry) or in
Philadelphia (humid)?
a) equally cool in both places
b) Philadelphia
c) Phoenix
In Phoenix, where the air is dry, more of the water will
evaporate from your skin. This is a phase change,
where the water must absorb the heat of vaporization,
which it takes from your skin. That is why you feel cool
as the water evaporates.
You’re in Hot Water!
Which will cause more severe
burns to your skin:
100 oC water or 100 oC steam?
a) water
b) steam
c) both the same
d) it depends...
Although the water is indeed hot, it releases only 1 cal/(g oC) of
heat as it cools. The steam, however, first has to undergo a
phase change into water and that process releases 540 cal/g,
which is a very large amount of heat. That immense release of
heat is what makes steam burns so dangerous.