Heating and Cooling Curves
Name_________________________
What happens when we heat a sample of ice that comes out of the deep freezer initially at −15°C? The addition of heat causes the
temperature of the solid ice to increase. As long as the temperature is below 0°C, the sample remains frozen. When the
temperature reaches 0°C (the melting point of water), the ice begins to melt. Because melting is an endothermic process, the heat
we add at 0°C is used to convert ice to water and the temperature remains constant until all the ice has melted. Once we reach this
point, any further addition of heat causes the temperature of the liquid water to increase. You observed a phase change process for
ice (solid water) being melted, heated and then boiled in class.
A graph of the temperature of the system versus the amount of heat added (or temp vs time if the heat is added at a constant rate)
is called a heating curve. We watched a heating curve form for water as it melted, then heated then began to vaporize. We
watched a cooling curve for para-dichlorobenzene as it these melted mothballs cooled down and then went through the freezing
process.
Understand each Segment on the Heating Curve below
AB
Heating ice from −15°C to 0°C is represented by
the sloping line segment AB. During this part of
the curve, the water is going though a kinetic
energy change.
BC
Converting the ice at 0°C to water at 0°C is the
horizontal segment BC. During this part of the
curve, the water is going though a potential energy
change.
CD
Additional heat increases the temperature of the
water until the temperature reaches 100°C during
segment CD. During this part of the curve, the
water is going though a kinetic energy change.
F
D
E
B
C
DE
The heat is then used to convert water to steam at
a constant temperature of 100°C during segment
DE. During this part of the curve, the water is
going though a potential energy change.
EF
The steam is then heated to its final temperature of 125°C in the sloping segment EF. During this part of the curve, the
water is going though a kinetic energy change.
A
Energy Calculations for the Sloping Segments of the Heating (or Cooling) Curve
We can calculate the energy change of the system for each of the segments of a heating curve. In segments AB, CD, and EF we
are heating a single phase from one temperature to another. The equation below can be used to calculate the amount of heat
needed to raise the temperature of a substance; the product of the specific heat capacity (c), mass, and temperature change. The
greater the specific heat of a substance, the more heat we must add to accomplish a certain temperature increase.
c × mass × ∆T = heat lost or gained
segment AB: 2.1 J/gºC × 10 g × 15ºC = 315 J
the H2O is ice so the SHC of ice must be used
segment CD: 4.18 J/gºC × 10 g × 100ºC = 4,180 J
the H2O is liquid so the SHC of liquid water must be used
segment EF: 1.7 J/gºC × 10 g × 25ºC = 425 J
the H2O is steam so the SHC of steam must be used
Because the specific heat of liquid water is greater than that of ice and steam, the slope of segment CD or EF is less than that of
segment AB; we must add more heat to water to achieve a 1°C temperature change than is needed to warm the same quantity of
ice or steam by 1°C.
Heating and Cooling Curves
(pg 2 of 2)
Energy Calculations for the Plateau Segments of the Heating (or Cooling) Curve
∆Hfusion and ∆Hvaporization
In segments BC and DE we are converting one phase to another at a constant temperature. The temperature remains constant
during these phase changes, because the added energy is used to overcome the attractive forces between molecules rather than to
increase their average kinetic energy. For segment BC, in which ice is converted to water, the enthalpy change can be calculated
by using ∆Hfus, while for segment DE we can use ∆Hvap Thus the equation for calculating the energy change during a phase
change is given below:
∆Hvap or fus × moles = heat lost or gained
kJ/mole × moles = kJ (kiloJoules)
be sure and notice that the units on the right side again cancel
out to equal the units on the left side of the equation.
Be sure and take note that in the equation above there is no ∆T because during a phase change, the substance remains at a constant
temperature (the plateau on the graph) and no temperature change occurs.
segment BC: 6.01 kJ/mole × 10 g × 1mole/18g = 3.34 kJ the phase change is solid to liquid so ∆Hfus must be used
OR
334 J/g × 10g = 3340 J or 3.34 kJ
segment DE: 40.7 kJ/mole × 10 g × 1mole/18g = 22.6 kJ
the phase change is liquid to gas so ∆Hvap must be used
(NOTE: This 40.7 kJ/mole is different than the 44 kJ/mole that you can calculate from the ∆Hf charts because
the 40.7 kJ/mole is for water at 100ºC, and the value calculated from the ∆Hf charts is for water at 25ºC)
OR
2261 J/g × 10 g = 22,610 J or 22.6 kJ
Both of the ∆Hphase change values above could be reported in different units:
∆Hvaporization = 334 J/g (This comes from 6.01 kJ/mol × 1mol/18g.)
∆Hfusion = 2261 J/g
(This can be calculated from 40.7 kJ/mol × 1mol/18g.)
The length of the plateau is directly related to the amount of heat required to make the phase change. If more substance was
making the phase change, the plateau would be longer.
Boiling Point - Melting Point
Using the word point can be a dangerous term
because it implies that melting or boiling occurs
instantaneously yet, from experience and from
the graph, you can see that in fact a substance
does not melt or boil (condense or freeze) at one
single point in one single moment, but rather it
takes a period of time to completely melt, boil
(condense or freeze)
Cooling Curves
Cooling a substance has the opposite effect of
heating it. Thus, if we start with water vapor and
begin to cool it, we would move right to left
through the events shown in the heating curve
above and redraw the curve as demonstrated
below.
Angle of the Sloping Segments
Remember the angle of the sloping portion is directly related to the specific heat capacity of the phase of the substance. Thus the
slope of the graph will be steeper for substances with a lower SHC.
Length of Plateau
Remember, the length of the plateau is directly related to the amount of heat required to make the phase change. For most
substances more heat is required to make the liquid to gas transition than is required to make the solid to liquid transition. The
energy required to make the solid to liquid transition is called the heat of fusion (∆Hfusion) and the energy required to make the
liquid to gas transition is called the heat of vaporization (∆Hvap). These values are unique to each particular substance and are
measured in kJ/mole (or J/g).