Phase Changes and Heating Curves
Phase Changes (or Phase Transitions)
The transformation of one state of matter into another state is called a phase transition or phase
change. See the image below. Phase transitions occur at very precise points, when the energy (measured
as temperature) of a substance in a given state exceeds that allowed in the state.
For example, liquid water can exist at a range of
temperatures. Cold drinking water may be around 4ºC.
Hot shower water has more energy and thus may be
around 40ºC. However, at 100°C under normal
conditions, water will begin to undergo a phase
transition into the gas phase. At this point, energy
introduced into the liquid will not go into increasing the
temperature; it will be used to send molecules of water
into the gas state. Thus, no matter how high the flame
is on the stove, a pot of boiling water will remain at
100ºC until all of the water has undergone transition to
the gas phase.
The excess energy introduced by a high flame will accelerate the liquid-to-gas transition; it will not
change the temperature. The heat curve below illustrates the corresponding changes in energy (shown in
calories) and temperature of water as it undergoes a phase transition between the liquid and gas states.
As seen in the graph below, as we move from left to right, the temperature of liquid water increases
as energy (heat) is introduced. At 100ºC, water begins to undergo a phase transition and the
temperature remains constant even as energy is added (the flat part of the graph). The energy that is
introduced during this period goes toward breaking intermolecular forces so that individual
water molecules can "escape" into the gas state. Finally, once the transition is complete, if more energy
is added to the system, the heat of the gaseous water, or steam, will increase.
This same process can be seen in reverse if we
look at the graph starting on the right side and
moving left. As steam is cooled, the movement of
gaseous water molecules and temperature will
decrease. When the gas reaches 100ºC,
more energy will be lost from the system as the
attractive forces between molecules reform;
however the temperature remains constant
during the transition (the flat part of the
graph). Finally, when condensation is complete,
the temperature of the liquid will begin to fall as
energy is withdrawn.
On warm days, water as a vapour
in the air will condense when it
touches the cool grass. The
water molecules loose energy as
they move from the gas phase to
liquid phase. Kinetic energy
changes to potential energy.
Phase transitions are an important part of the world around us. For example, the energy withdrawn when
perspiration evaporates from the surface of your skin allows your body to correctly regulate its
temperature during hot days. Phase transitions play an important part in geology,
influencing mineral formation and possibly even earthquakes. And who can ignore the phase transition
that occurs at about -3ºC, when cream, perhaps with a few strawberries or chocolate chunks, begins to
form solid ice cream.
Now we understand what is happening in a pot of boiling water. The energy (heat) introduced at the
bottom of the pot causes a localized phase transition of liquid water to the gaseous state. Because gases
are less dense than liquids, these localized phase transitions form pockets (or bubbles) of gas, which rise
to the surface of the pot and burst. But nature is often more magical than our imaginations. Despite all
that we know about the states of matter and phase transitions, we still cannot predict where the
individual bubbles will form in a pot of boiling water.
Difference between evaporation and boiling:
Evaporation
Boiling
Vapour pressure measures the tendency for the
molecules to escape from liquid to the gas phase. At
lower temperatures the vapour pressure of a liquid
is much lower than the pressure on the surface of
the liquid. When the temperature of the liquid is
gradually increased, its vapour pressure also
increases. Ultimately a stage is reached when the
vapour pressure of the liquid equals the pressure of
the air above it. At this point, molecules and
vapours formed within the liquid can easily rise
through the liquid in the form of bubbles and
escape into the air. This phenomenon is known as
boiling and the temperature at which this occurs is
known as boiling point.
Boiling point is the temperature at which the vapour
pressure of a liquid becomes equal to the
atmospheric pressure. The boiling point, therefore,
depends upon the atmospheric pressure and it
changes with the change in the pressure above the
liquid. As the atmospheric pressure increases, it is
necessary to heat the liquid to a higher
temperature to make its vapour pressure equal to
atmospheric pressure. At high altitudes, having
lower atmospheric pressure, water boils at a much
lower temperature than in the plains where
atmospheric pressure is higher.
Once the boiling starts, the temperature of the
liquid remains constant, until the whole of the liquid
has vaporized, even though heating is continued.
Heating Curve of a Pure Substance
* As the temperature increases, potential
energy changes to kinetic energy
* Endothermic process; energy is absorbed
Cooling Curve of a Pure Substance
* As the temperature decreases, kinetic
energy changes to potential energy
* Exothermic process; energy is released
s
Graph
Explanation
Section
*pure solid has an increase in temperature
A-B
Q = mc∆T (∆T= Tfinal - Tinitial)
*phase change; solid changing to liquid
B-C
*melting point; this is the temperature at
which the pure substance will melt
∆H = mHf (Hf is the heat of fusion)
*pure liquid has an increase in temperature
C-D
Q = mc∆T
*phase change; liquid changing to gas
D-E
*boiling point; this is the temperature at
which the pure substance will boil
∆H = mHv (Hv is the heat of vaporization)
*pure gas has an increase in temperature
E-F
Q = mc∆T
∆H and Q both represent energy in either the unit of
calories or Joules
HEAT CAPACITY (c) OF WATER
liquid: 4.184 J/g °C
solid: 2.03 J/g °C
gas: 2.01 J/g °C
VALUES FOR WATER
latent heat of fusion Hf: 334 J/g
latent heat of vaporization Hv: 2260 J/g
Graph
Explanation
Section
*pure gas has a decrease in
P-Q
temperature
Q = mc∆T (∆T= Tfinal - Tinitial)
*phase change; gas changing to liquid
Q-R
*condensation point; this is the
temperature at which the pure
substance will condense from a gas to a
liquid (same temperature as when it
boils)
∆H = mHv (Hv is the heat of
vaporization)
*pure liquid has a decrease in
R-S
temperature
Q = mc∆T
*phase change; liquid changing to solid
S-T
*freezing point; this is the temperature
at which the pure substance will freeze
(same temperature as when it melts)
∆H = mHf (Hf is the heat of fusion)
*pure solid has a decrease in
T-D
temperature
Q = mc∆T
∆H and Q both represent energy in either the unit
of calories or Joules
EXAMPLE #1: Calculate the amount of heat required to completely convert 50 g of ice
at -10 ºC to steam at 120 ºC. Sketch a graph of this change, provide an appropriate
title and label both the x and y axis with the correct units.
SOLUTION: This is a heating curve. Heat is taken up in five stages. The heat taken up in the
complete process is the sum of the heat taken up in each stage. Endothermic process.
1. (A–B) Heat taken up as ice
heats from -10 ºC to the
melting point, 0 ºC.
Q = mc∆T (A–B)
Q = mass of water x specific heat ice x temperature change
Q = 50 g x 2.03 J/gºC x 10 ºC
Q = 1015 J
2. (B-C) Heat taken up to
∆H = mHf (B-C)
convert ice to water (melting). ∆H = mass of water x latent heat of fusion
Phase change occurring.
∆H = 50 g x 334 J/g
∆H = 16700 J
3. (C-D) Heat taken up by
liquid water from 0 ºC to the
boiling point, 100 ºC.
Q = mc∆T (C-D)
Q = mass of water x specific heat liquid water x temp. change
Q = 50 g x 4.184 J/gºC x 100 ºC
Q = 20900 J
4. (D-E) Heat taken up
vaporizing the water (boiling).
Phase change occurring.
∆H = mHV (D-E)
∆H = mass of water x latent heat of vaporization
∆H = 50 g x 2260 J/g
∆H = 113000 J
5. (E-F) Heat taken up as the Q = mc∆T (E-F)
NOTE: water vapour = steam
steam (gas) heats from 100 ºC Q = mass of water x specific heat water vapour x temp. change
to 120 ºC.
Q = 50 g x 2.01 J/gºC x 20 ºC
Q = 2010 J
The sum of these is:
1015 J + 16700 J + 20900 J+ 113000 J + 2010 J
= 153625 J
approximately 154 kJ NOTE: 1000 kJ = 1 J
EXAMPLE #2: Calculate the amount of heat lost when 13 g of water vapour (steam) at
103 ºC changes to ice at -4 ºC. Sketch a graph of this change, provide an appropriate
title and label both the x and y axis with the correct units.
SOLUTION: This is a cooling curve. Heat is lost in five stages. The heat released in the
complete process is the sum of the heat lost in each stage. Exothermic process so each
calculation in the five steps results in a negative value - indicating the loss of heat.
1. (A–B) Gas (or steam) loses
Q = mc∆T (A–B)
heat as it cools from 103 ºC to Q = mass of water x specific heat steam x temperature change
100 ºC.
Q = 13 g x 2.01 J/gºC x (-3 ºC)
Q = -78 J
2. (B-C) Heat lost as gas
condenses to liquid. Phase
change occurring.
∆H = mHv (B-C)
∆H = mass of water x latent heat of vapourization
∆H = 13 g x (- 2260 J/g)
∆H = -29380 J
3. (C-D) Heat lost as the
Q = mc∆T (C-D)
water cools from 100 ºC to the Q = mass of water x specific heat liquid water x temp. change
freezing point of 0 ºC.
Q = 13 g x 4.184 J/gºC x (-100 ºC)
Q = -5439 J
4. (D-E) Heat lost as water
freezes. Phase change
occurring
∆H = mHf (D-E)
∆H = mass of water x latent heat of fusion
∆H = 13 g x (-334 J/g)
∆H = -4342 J
5. (E-F) Heat lost as ice cools
from 0 ºC to -4 ºC.
Q = mc∆T (E-F)
Q = mass of water x specific heat ice x temp. change
Q = 13 g x 2.03 J/gºC x (-4 ºC)
Q = -106 J
The sum of these is:
(-78 J) + (-29380 J) + (-5439 J) + (-4342 J) + (-106 J)
= 39345 J approximately 39 kJ