George Washington ran
a distillery at his Mount
Vernon estate.
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If thermal energy is added to the
water at a rate of 84 W, how much
time would it take to bring the vat
of water from room temperature
(21.0°C) to boiling (100.0°C)?
Warm-up: 2/6/15
The vats where water
was heated held 795 L
of water. The current
method of heating the
water is through the use
of an immersion
heater—hot wires with
current running through
them that have been
submersed in the water.
LATENT HEAT AND PHASE CHANGES
A.S. 3.1.8 – 3.1.15 Due Thursday 2/12
There will be a quiz on Thursday
INTERNAL ENERGY
• The total of the potential energy and random kinetic energy of
all the particles in the substance
• Potential energy comes from bonds and intermolecular
forces
• Typically, within a particular phase, the farther apart the
molecules/atoms are, the higher the potential energy will
be
• Average kinetic energy of the particles in the substance is
related to the absolute (Kelvin) temperature of the substance
SKIT ASSIGNMENT
• Groups assigned
• Create a skit to model the molecular behavior of the 3
main states of matter as the temperature rises
MACROSCOPIC CHARACTERISTICS OF MATTER
Solid
Shape
Volume
Compressibility
Diffusion
Liquid
Gas
MICROSCOPIC CHARACTERISTICS OF MATTER
Solid
Kinetic Energy
Potential Energy
Mean molecular
separation
Molecules per m3
Liquid
Gas
WARM-UP: 2/9/15
Copy the diagram,
and label each arrow
with the correct name
for the phase change
that occurs in the
direction indicated:
SOLID
LIQUID
GAS
QUANTIFYING PHASE CHANGES
• Latent Heat:
• The energy required to achieve the change of phase of a
substance
• Energy added/removed is used to change the potential energy of
the particles in the substance.
• The average kinetic energy remains constant, which means that
the temperature will remain constant throughout the entirety of the
phase change
QUANTIFYING PHASE CHANGES
• Specific Latent Heat of Fusion
• The energy required to change the phase of 1 kg of
substance from a solid to a liquid without any temperature
change
• Add energy  melt
• Remove energy  freeze
QUANTIFYING PHASE CHANGES
• Specific Latent Heat of Vaporization
• The energy required to change the phase of 1 kg of
substance from a liquid to a gas without any temperature
change
• Add energy  vaporize
• Remove energy  condense
QUANTIFYING PHASE CHANGE
∆𝑄 = 𝑚𝐿
• Q = thermal energy added or removed (depending on phase change)
• Units typically in joules / J
• m = mass / kg
• L = specific latent heat / J·kg -1
• 𝐿𝑓  specific latent heat of fusion
• 𝐿𝑣  specific latent heat of vaporization
SAMPLE PROBLEM
• 2.0 kg of solid water (ice) at exactly 0.0 °C is to be changed into liquid
water at this temperature. Calculate the amount of energy needed to
be added to the water to melt it.
• (Lf = 3.34 x 105 J kg-1 )
• How much energy is required to raise the temperature of the same 2.0
kg of water, now that it’s fully melted, to its boiling point?
• The same 2.0 kg of water now is boiled until it vaporizes completely
into steam at 100. °C. How much energy must be added to the water
to just vaporize it?
• (Lv = 2.26 x 106 J kg-1)
LATENT HEAT AND CALORIMETRY
• Quite often, total energy added involves both specific heat and
specific latent heat quantities.
• For example, similar to the previous sample:
“How much energy must be added to a 3.2 kg of sample of ice,
originally at 0.0°C, so that it becomes steam at 115.0 °C?”
• Turn to you neighbors: 1 minute—discuss how you would
approach this problem
PROBLEM SOLVING TIPS WHEN PROBLEMS
INCLUDE SPECIFIC HEAT AND LATENT HEAT
• Make a column for each change that is occurring as the energy is
added or removed.
• A change is either: phase change or change in temperature
• Put a brief heading at the top of each column (i.e. “melt” “liquid water”
“vaporize”)
• Under the description, write the equation that you will use to find the
thermal energy for that segment
• Write your variables and constants for each column that you will use in
the equations you listed.
• Solve for each individual amount of energy
• Add them all together! (and circle your answer…you’re done!)
CALORIMETRY EXAMPLE
• Steam at 100°C is bubbled into 0.330 kg of water at 30°C in a
calorimeter cup. How much steam will have been added when the
water in the cup reaches 51°C? (Ignore the effect of the cup.)
• Step 1: 2 columns gaining energy and losing energy
• Step 2: In each column, determine if there is a temperature
change or phase change occurring
• Step 3: Set up the values (energy gained = energy lost) as you
would under a calorimetry problem involving only temperature
changes, but this time you’ll have a phase change to deal with as
well.
STEAM AT 100.°C IS BUBBLED INTO 0.330 KG OF WATER AT 30.0°C
IN A CALORIMETER CUP. HOW MUCH STEAM WILL HAVE BEEN
ADDED WHEN THE WATER IN THE CUP REACHES 51.0°C?
(IGNORE THE EFFECT OF THE CUP.)
Losing Energy
Gaining Energy
Steam condensing
Hot water cooling
Cool water warming
Q = mLv
Q = mcDT
Q = mcDT
m = ??
m = ??
m = 0.330 kg
L = 2.26 x 106 J kg-1
c = 4186 J kg-1 °C-1
c = 4186 J kg-1 °C-1
Ti = 100. °C
Ti = 30.0 °C
Tf = 51.0 °C
Tf = 51.0 °C
STEAM AT 100.°C IS BUBBLED INTO 0.330 KG OF WATER AT 30.0°C
IN A CALORIMETER CUP. HOW MUCH STEAM WILL HAVE BEEN
ADDED WHEN THE WATER IN THE CUP REACHES 51.0°C?
(IGNORE THE EFFECT OF THE CUP.)
𝑚𝐿𝑣 + 𝑚𝑐∆𝑇 = 𝑚𝑐∆𝑇
𝑚 2.26𝑥106 + 𝑚 4186 (100.0 − 51.0) = (0.330)(4186)(51.0 − 30.0)
𝑚 2.26𝑥106 + (𝑚)(205114) = 29009
𝑚 2465114 = 29009
𝒎 = 𝟎. 𝟎𝟏𝟏𝟖 𝒌𝒈
SAMPLE PROBLEM #3
• A volume of 0.80 L of water at 19°C is put into an aluminum icecube tray of mass 0.210 kg at the same temperature. How much
energy must be removed from this system by the refrigerator to
turn the water into ice at -9.0°C?