12.8 Heat and Phase Change: Latent Heat
• Glass of ice water at 0
C. Heat is being used
to melt ice, and then
only when all the ice is
melted will the
temperature of the
liquid begin to rise.
Heat and Phase Change: Latent Heat
• A solid can melt or fuse into a liquid if heat is
added.
• Liquid can freeze into a solid if heat is removed.
• A liquid can evaporate into a gas if heat is
supplied.
• Gas can condense into a liquid if heat is taken
away.
• Rapid evaporation, formation of vapor bubbles
within the liquid is called boiling.
• A solid can change directly into a gas if that is
provided, called sublimation.
• Example: dry ice (CO )
• Solid naphthalene
(moth balls) turns into
naphthalene fumes.
• http://www.youtube.co
m/watch?v=cTP4yp8y_
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Conceptual Example 13: Saving Energy
Suppose you are cooking spaghetti for dinner,
and the instructions say “boil the pasta in
water for ten minutes.” To cook spaghetti in an
open pot with the least amount of energy,
should you turn up the burner to its fullest so
the water vigorously boils, or should you turn
down the burner so the water barely boils?
Latent Heat
• Heat needed for a phase change.
• A substance changes from one phase to
another, the amount of heat that must be
added or removed depends on the type of
material and the nature of the phase change.
The heat Q that must be supplied or removed to change the phase of a mass m of a
substance is.
Q = mL
Where L is the latent heat of the substance. SI Unit of Latent Heat: j/kg
Latent Heat
• Latent heat of fusion: Lf, refers to the change
between solid and liquid phases.
• Latent heat of vaporization Lv, change between
liquid and gas phases.
• Latent heat of sublimation Ls: change between
solid and gas phases.
• Lf = 3.35 x 10^5 J/kg water
• So 3.35 x 10^5 J/kg of heat must be supplied to
melt one kilogram of ice at 0 C.
• This amt. of heat must be removed from one
kilogram of liquid water at 0 C to freeze the liquid
into ice.
• Latent heat of vaporization for water has the
much larger value of Lv = 22.6 x 10^5 J/kg
• When water boils at 100 C, 22.6 x 10^5 J of
heat must be supplied for each kilogram of
liquid turned into steam.
• When steam condenses at 100 C, this amt. of
heat is released from each kilogram of steam
that changes back into liquid.
In the Real World
• Designers can engineer clothing that can absorb
or release heat to help maintain a comfortable
and constant temperature close to your body.
• PCM “phase change material”
• Prevents overheating by melting, absorbing
excess body heat in the process.
• PCM freezes and releases heat to keep you warm.
http://www.newlaunches.com/archives/nike_pre
cool_vest.php
Example 14: Ice-Cold Lemonade
Ice at 0 C is placed in a styrofoam cup containing
0.32 kg of lemonade at 27 C. The specific heat
capacity of lemonade is virtually the same as that
of water; that is, c = 4186 J/(kgxC). After the ice
and lmonade reach an equilibrium temperature,
some ice still remains. The latent heat of fusion
for water is Lf = 3.35 x 10^5 J/kg. Assume that
the mass of the cup is so small that it absorbs a
negligible amount of heat, and ignore any heat
lost to the surroundings. Determine the mass of
ice that has melted.
Example 15: Getting Ready for a Party
A 7.00kg glass bowl (c = 840 J/(kgxC)) contains 16.0kg of
punch at 25 C. Two and a half kilograms of ice [c=2.00
x 10^3J/(kgxC0] are added to the punch. The ice has
an initial temperature of -20.0 C, having been kept in a
very cold freezer. The punch may be treated as if it
were water [c = 4186J/(kgxC)], and it may be assumed
that there is no heat flow between the punch bowl and
the external environment. The latent heat of fusion for
water is 3.35 x 10^5 J/kg. When thermal equilibrium is
reached, all the ice has melted, and the final
temperature of the mixture is above 0 C. Determine
this temperature.
Practice Problem
52. To help prevent frost damage, fruit growers
sometimes protect their crop by spraying it with water
when overnight temperatures are expected to go
below the freezing mark. When the water turns to ice
during the night, that is released into the plants,
thereby giving them a measure of protection against
the falling temperature. Suppose a grower sprays 7.2
kg of water at 0 C onto a fruit tree. (a) How much heat
is released by the water when it freezes? (b) How
much would the temperature of a 180 kg tree rise if it
absorbed the heat released in part (a)? Assume that
the specific heat capacity of the tree is 2.5 x 10^3 J/kgC
and that no phase change occurs within the tree itself.
Homework pg. 391 ch. 12
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12.9 Equilibrium Between Phases of Matter
• Under specific conditions of temperature and
pressure, a substance can exist at equilibrium in
more than one phase at the same time.
• Ex. Container kept at a constant temp. by a large
reservoir of heated sand. Partially filled with a
liquid and a few fast-moving molecules escape
the liquid and form a vapor phase.
• Molecules pick up the required energy (the latent
heat of vaporization) during collisions with
neighboring molecules in the liquid.
• The reservoir of heated sand replenishes the energy carried
away, thus maintaining the constant temperature.
• At first, the movement of molecules is predominantly from
liquid to vapor, although some molecules in the vapor
phase do reenter the liquid.
• As the molecules accumulate in the vapor, the number
reentering the liquid eventually equals the number
entering the vapor, at which point equilibrium is
established, as in part b.
• The concentration of molecules in the vapor phase does
not change, and the vapor pressure remains constant.
• The pressure of the vapor that coexists in equilibrium with
the liquid is called the equilibrium vapor pressure of the
liquid.
• Equilibrium vapor pressure does not depend on
the volume of space above the liquid.
• If more space were provided, more liquid would
vaporize, until equilibrium was reestablished at
the same vapor pressure, assuming the same
temperature is maintained.
• Equilibrium vapor pressure depends only on the
temperature of the liquid; a higher temp. causes
a higher pressure.
• Only when the temperature and vapor
pressure correspond to a point on the curved
line, which is called the vapor pressure curve
or the vaporization curve, do liquid and vapor
phases coexist at equilibrium.
• Boiling to occur, the pressure of the vapor inside them
must at least equal the air pressure acting on the
surface of the water.
• Atmosphere 1.01 x 10^5 Pa
• 1.01 x 10^5 Pa corresponds to a temperature of 100 C.
• Water boils at 100 C at one atmosphere of pressure.
• Liquid boils at the temperature for which its vapor
pressure equals the external pressure.
• So if the atmospheric pressure goes down the boiling
point goes down.
• Water does boil at 83 C on a mountain at an
altitude of just under five kilometers, because
atmospheric pressure there is 0.53 x 10^5 Pa.
• Spray cans lowers the pressure inside the can
so that the liquid comes out like a vapor.
• For each temperature, there is a single
pressure at which the two phases can coexist
in equilibrium.
• Fusion curve: a plot of the equilibrium
pressure versus equilibrium temperature.
12.10 Humidity
• Air is a mixture of gases, including nitrogen,
oxygen, and water vapor.
• Total pressure of the mixture is the sum of the
partial pressures of the component gases.
• The partial pressure of a gas is the pressure it
would exert if it alone occupied the entire
volume at the same temperature as the
mixture.
• The partial pressure of water vapor in air depends
on weather conditions.
• Relative humidity: amt. of water vapor is in the air.
Ratio of the partial pressure of water vapor in the
air to the equilibrium vapor pressure at a given
temperature.
Percent
partial pressure of water vapor
Relative
= equilibrium vapor pressure of
x100
Humidity
water at the existing temperature
• Vaporization curve of water gives the equilibrium
vapor pressure of water at the existing
temperature.
• When the partial pressure of the water vapor
equals the equilibrium vapor pressure of water at
a given temperature, the relative humidity is
100%.
• Vapor is said to be saturated because it is present
in the maximum amount, as it would be above a
pool of liquid at equilibrium in a closed container.
• If the relative humidity is less than 100%, the
water vapor is said to be unsaturated.
Example 17: Relative Humidities
One day, the partial pressure
of water vapor in the air is
2.0 x 10^3 Pa. Using the
vaporization curve for
water in Figure 12.37,
determine the relative
humidity if the
temperature is (a) 32 C and
(b) 21 C.
Practice Problem 85.
Suppose that air in the human lungs as a
temperature of 37 C, and the partial pressure
of water vapor has a value of 5.5 x 10^3 Pa.
What is the relative humidity in the lungs?
Consult the vapor pressure curve for water
that accompanies problem 68.
85.
54.