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 = mcΔT
specific heat
capacity
Common Unit for Specific
Heat Capacity: J/(kg·Co)
OTHER UNITS
1 kcal = 4186 joules
1 cal = 4.186 joules
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.
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 440 J/(kg ∙ oC) and that of
sphere B is 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
(mcΔT )Al + (mcΔT )water
(mΔT )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?