Thermal Capacity
Of a particular body is the energy required to raise the temperature of that body by 1°C.
Thermal capacity =
change in thermal energy
temperature change
C = ∆Q / ∆T
Example 1
A 2 kg cylinder of copper is heated from room temperature (20˚C) to 500ºC. 374kJ of thermal energy
were transferred to the copper during the heating process. Calculate the thermal capacity of this piece
of copper.
Answer: 780J
Example 2
A 25kg cylinder
of copper is heated from room temerature. The same 374kJ of thermal energy were
used during the heating process but this time the copper’s temperature rose from room temperature
to only 58.4ºC. Calculate the heat capacity of this piece of copper.
Answer:
9740J What is the difference between Ex 1 and Ex2
Specific Heat
Adding energy to a material causes the temperature to go up.
Taking energy away from a substance causes the temp. to go down!
Have you ever noticed that on a hot summer day the pool is coo
ler than the hot cement?
OR maybe
that the ocean is cooler than the hot sand?
Why? The sun has been beating down on both of them for
the same amount of time...........
It takes more thermal energy to raise the temperature of water
that it does the cement!
Specific Heat
The amount of energy required to raise the temperature of a material (substance).
It takes different amts of energy to make the same temp change in different substances.
The specific heat capacity of a particular substance is equal to the
energy required to raise the
temperature of a 1kg mass of the substance by 1ºC
Specific Heat of water
The Cp is high because H
2
O mols. form strong bonds w/each other.
It takes a lot of energy to break the bonds so that the the
molecules can then start to move around
faster (HEAT UP).
Example:
Specific Heat of Water
Cp = 4,184 Joules of energy to raise the temperature of 1kg 1°C.
Example 3
A 2kg cylinder of copper is heated from room temperature(20ºC) to 500ºC. 374kJ of thermal
energy
were transferred to the copper during the heating process. Calculate the specific heat capacity of this
piece of copper.
Answer: 390J
Example 3
A 2kg cylinder of copper is heated from room temperature(20ºC) to 500ºC. 374kJ of thermal energy
were
transferred to the copper during the heating process. Calculate the specific heat capacity of this
piece of copper.
Answer: 390J
Example 4
A 25kg cylinder of copper is heated from room temerature. The same 374kJ of thermal energy were
used during the he
ating process but this time the copper’s temperature rose from room temperature
to only 58.4ºC. Calculate the specific heat capacity of this piece of copper.
Answer: 390J
Solving for specific heat
There are two methods common for measuring the specific h
eat capacity.
Electrical
–
If an electrical immersion heater is place into a solid or a liquid, then the energy from
the heater will be transmitted by conduction into the substance and the substance will get hotter.
Mixtures
–
If a hot object is place next
to a cooler one (or placed into it if the cooler one is liquid),
then the cooler substance will gain energy and become hotter and the hotter object will lose
energy and become cooler until both objects come to the same temperature called thermal
equilibri
um.
Example 5
–
electrical
A 240V electric heating element is used to heat water. The temperature of the water rose from 20ºC to
50ºC in 4minutes 20 seconds. During the heating process, the current flowing in the heater was
measured to be 3.54A. Calcula
te the mass of the water.
Solution
First the power rating is Power = Voltage x Current
P = V I (I.B. Data booklet page 7)
P = 240 x 3.54 = 850W
The heater supplies 850J of energy to the water every second (850W= 850J/s). So in 4minutes
20seconds(260s),
energy transferred to the water = 850 x 260 = 221x10
3
J.
Answer: 1.75kg
Example 6
The 850W heater was then placed into a hole in a piece of copper of mass 1.75kg. (A) Calculate the
temperature rise in the copper if the heater was left on for 4min 20sec.
(B) Calculate the final
temperature of the copper if the heater was left on for 10min and the copper was originally at a
temperature of 65ºC.
Answer: (A) = 324ºC, (B) = 747ºC
Example 7
–
Mixture
A block of substance “X” has a mass of 100g and is heated to
260ºC. The block is then placed into a
beaker containing 500g of water at 20ºC. After some time both substances reach their equilibrium
temperature of 30ºC. Calculate the specific heat capacity of substance X.
Solution: Energy gained by the water = Energ
y lost by X
Q
w
= Q
x
m
w
c
w
∆
T
w
= m
x
c
x
∆
T
x
Answer = c
x
= 913J/kgºC
Example 8
How much energy is needed to heat a 1kg aluminum pan containing 2kg of water from 25ºC to 95ºC?
Solution: Total Energy = Energy gained by aluminum + Energy gained by water
Answer 6
51kJ
Example 9
A 0.5kg block of copper (specific heat capacity 390J/kgºC) at an initial temperature of 420ºC was
placed into 1.3kg of water at 40ºC. What will be the final temperature of the mixture when thermal
equilibrium is reached?
Answer: T
final
=
53.1ºC
Micro Properties of different phases
Solids
Strong bonds between atoms
Lowest internal energy
Atoms in fixed positions vibrating/oscillating
Liquids
Weaker forces. Some bonds are broken
More internal energy
Atoms can move about and change places
Gases
Virtually no forces/bonds
High internal energy
Atoms completely free to move at high speed
Macro Properties of different phases
Solids
Maintain shape
Lowest temp
Low compression/expansion
Liquids
Takes the shape of its container
Moderate temp
Low
compression/expansion
Gases
Fills the container
Highest temp
High compression/expansion
Plasmas
–
atoms are at extremely high temperatures and are ionized.
Usually found in stars.
Substance
Specific Heat(J/kg.
°C)
Specific Heat of
Beryllium
1830
Specific Heat of Cadmium
230
Specific Heat of Copper
387
Specific Heat of Germanium
322
Specific Heat of Gold
129
Specific Heat of Iron
448
Specific Heat of Lead
128
Specific Heat of Silicon
703
Specific Heat of Silver
234
Specific Heat of Brass
380
Specific Heat of Glass
837
Specific Heat of Ice(
-
5°C)
2090
Specific Heat of Marble
860
Specific Heat of Wood
1700
Specific Heat of Alcohol(ethyl)
2400
Specific Heat of Mercury
140
Specific Heat of Water(15°C)
4186
Specific Heat of Steam(100°C)
2010
Specific Heat of Aluminium
900
Specific Heat of Tin
540
Specific Heat of Steel
120
Specific Heat of Sand
830
Specific Heat of Ethanol (Alcohol, ethyl
32°F)
2.3 K
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