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 cooler 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 H2O 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 heating 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 heat 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
equilibrium.
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. Calculate 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 = 221x103J.
 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 = Energy lost by X
 Qw = Qx
 mwcw∆Tw = mxcx∆Tx
 Answer = cx = 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 651kJ
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: Tfinal = 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 of Beryllium
Specific Heat of Cadmium
Specific Heat of Copper
Specific Heat of Germanium
Specific Heat of Gold
Specific Heat of Iron
Specific Heat of Lead
Specific Heat of Silicon
Specific Heat of Silver
Specific Heat of Brass
Specific Heat of Glass
Specific Heat of Ice(-5°C)
Specific Heat of Marble
Specific Heat of Wood
Specific Heat of Alcohol(ethyl)
Specific Heat of Mercury
Specific Heat of Water(15°C)
Specific Heat of Steam(100°C)
Specific Heat of Aluminium
Specific Heat of Tin
Specific Heat of Steel
Specific Heat of Sand
Specific Heat of Ethanol (Alcohol, ethyl
32°F)
Specific Heat(J/kg.
°C)
1830
230
387
322
129
448
128
703
234
380
837
2090
860
1700
2400
140
4186
2010
900
540
120
830
2.3 K