Specific Heat Capacity
and Latent Heat
AS level Physics Notes on:
“Calculations involving change of energy
DQ = mcDq where m is the mass of the substance, c is its specific
heat capacity and Dq is the change in temperature
DQ = ml where l is specific latent heat and m is the mass of
substance changing state. “
A Level Physics
LOJ March 2004
Heat Travel Revision
• Heat travels from hot to cold
• The bigger the temperature
difference the faster the rate of
transfer
A Level Physics
LOJ March 2004
Internal Energy
• The internal energy (sometimes called
the random thermal energy) of a
substance is the sum of
– the kinetic energy and
– the potential energy
of its particles.
A Level Physics
LOJ March 2004
Internal Energy
• Potential energy is due to the
interaction of neighbouring particles.
• This is therefore very significant in
solids and liquids but less so in gases.
• In fact ideal gases have NO
potential energy – just kinetic!
A Level Physics
LOJ March 2004
Internal Energy
• Kinetic energy is due to the
movement of the particles in the
substance.
• The faster they move
– the higher the KE and
– the higher the temperature
A Level Physics
LOJ March 2004
Specific Heat Capacity
• When you give heat energy to a
substance it gets hotter if the heat
is used to increase the KE of the
particles.
• How much hotter depends on two
things:
– Its mass and
– What it is made of
A Level Physics
LOJ March 2004
Specific Heat Capacity
• It makes sense that
– the more of it you have the more energy you
would have to give it to raise the temperature a
certain amount of a substance and that
– different materials would need different
amounts of heat to get hotter as their
structure and the number of particles in a
certain mass is different for each type.
• Values are therefore quoted for the heat
needed to raise the temperature of 1kg of
a substance by 1K
A Level Physics
LOJ March 2004
The Equation
DQ = mcDq
m = mass (kg)
c = specific heat capacity (J kg-1 K-1)
Q = heat energy (J)
q = temperature (K)
The D means ‘difference in’ because if you put
heat in you get an increase – if heat comes out
of the system the temperature goes down. You
can therefore use signs to indicate gain or loss.
A Level Physics
LOJ March 2004
Definition
• The Specific Heat Capacity (c) of a
substance is the quantity of energy
required to raise the temperature of
1kg of the substance by 1K.
A Level Physics
LOJ March 2004
SHC - c
• The biggest changes in temperature
of a given mass of a substance will
occur in those that have low specific
heat capacities - because it doesn't
take much energy for them to get
hotter!
A Level Physics
LOJ March 2004
Water
• Water has a very large SHC
• 4200 J kg-1 K-1
• This is about ten times that of a
metal.
A Level Physics
LOJ March 2004
Water
• It makes an excellent heat store.
• To store heat you want the thing it is
stored in not to get too hot – otherwise it
will lose heat very quickly to the
surroundings – remember heat loss to the
surroundings depends on the diference in
temperature between the object and its
surroundings (DT)
A Level Physics
LOJ March 2004
Water
• Water has a large SHC
• Therefore is makes an excellent coolant.
• A good coolant will take a lot of heat away
from whatever you are trying to cool
without getting too hot itself.
• Once the coolant is the same temperature
as the thing you want cooling it will stop
taking heat from it!
A Level Physics
LOJ March 2004
Latent Heat
• Means ‘hidden heat’
• Is absorbed or evolved when a substance
changes state.
• Doesn’t result in a change of temperature.
• Some substances require more energy per
kilogram to change the degree of freedom
of their particles than others.
• Relates to internal potential energy NOT
the average kinetic energy of particles
A Level Physics
LOJ March 2004
Heating Ice
• If ice is heated
steadily and its
temperature recorded
at regular intervals an
interesting graph is
obtained.
A Level Physics
LOJ March 2004
A Level Physics
LOJ March 2004
Latent Heat – hidden heat that does not
register as a temperature rise
• Thus heat is used to raise the temperature
of something if it is not changing state.
• If it IS changing state then that energy is
used for that purpose and the substance
does not get any hotter.
• It gives the particles in the substance
more ‘freedom’ rather than increasing their
kinetic energy.
• It is increasing their potential energy – the
internal energy of the substance.
A Level Physics
LOJ March 2004
Work
• The heat energy is used to do work
against intermolecular forces.
• In substances that expand when they
change state (not always the case!)
the energy is used to do work against
external forces
A Level Physics
LOJ March 2004
Equation
• It makes sense that the more of the substance
you have to melt/boil the more energy you will
have to supply.
• Therefore we have quoted values for how much
energy is required to change the state of one
kilogram of various substances
• As the values relate to 1kg the values are termed
as the specific latent heat – symbol l (for latent!)
• The unit of l is therefore J/kg
DQ = ml
A Level Physics
LOJ March 2004
Equation
DQ = ml
l = specific latent heat (J/kg)
m = mass (kg)
Q = Heat energy (J)
The D indicates that heat can be input to
change ‘up’ a state or given out when a
substance changes ‘down’ a state
A Level Physics
LOJ March 2004
Definitions
• Specific latent heat is the energy
required to change the state of 1 kg of a
substance.
• Specific latent heat of fusion is the
energy required to change the state of 1 kg
of a substance form a solid to a liquid.
• Specific latent heat of vaporisation is the
energy required to change the state of 1 kg
of a substance form a liquid to a gas.
A Level Physics
LOJ March 2004
Calculations
• The layout of calculations is important
• Think about what is happening.
– What gains energy?
– What loses energy?
– List the energy gains and losses then equate
them.
• Use symbols for the unknowns and the
answer will ‘all come out in the wash’!
A Level Physics
LOJ March 2004
Example
• A kettle of power 2kW holds 2 litres
of water at room temperature – 20oC.
• If the kettle is left on for 5 minutes
will it boil dry?
• Cwater = 4200 J kg-1 K-1
• l water = 2260 kJ kg-1
A Level Physics
LOJ March 2004
A kettle of power 2kW holds 2 litres of water at room temperature – 20oC.
If the kettle is left on for 5 minutes will it boil dry?
Cwater = 4200 J kg-1 K-1
lwater = 2260 kJ kg-1
• Where does the energy given to the water
come from?
• The electricity supply via the kettle’s
electrical element
• How much energy is given to the water?
• 2000 J every second for 5 minutes
• Calculate this!
• 2000 x 5 x 60 = 6 x 105 J
A Level Physics
LOJ March 2004
A kettle of power 2kW holds 2 litres of water at room temperature – 20oC.
If the kettle is left on for 5 minutes will it boil dry?
Cwater = 4200 J kg-1 K-1
lwater = 2260 kJ kg-1
• Energy input = 6 x 105 J
• How much energy is required to bring the water to
boiling point?
• What equation do we need?
DQ = mcDq
• Okay, so how much energy is needed?
• (Remember that 1 litre of water has a mass of 1kg
and the SHC of water is 4200 J kg-1 K-1)
• Q = 2 X 4200 X 80 = 6.72 x 105 J
A Level Physics
LOJ March 2004
A kettle of power 2kW holds 2 litres of water at room temperature – 20oC.
If the kettle is left on for 5 minutes will it boil dry?
Cwater = 4200 J kg-1 K-1
lwater = 2260 kJ kg-1
• Energy input = 6 x 105 J
• Energy required to boil the water =
6.72 x 105 J
• What does this mean?
• The water wouldn’t even boil – let
alone boil dry!
A Level Physics
LOJ March 2004
A kettle of power 3kW holds 2 litres of water at room temperature – 20oC.
If the kettle is left on for 5 minutes will it boil dry?
Cwater = 4200 J kg-1 K-1
lwater = 2260 kJ kg-1
• What would happen if the power of
the kettle used was 3kW instead?
• Try it yourself!
A Level Physics
LOJ March 2004
A kettle of power 3kW holds 2 litres of water at room temperature – 20oC.
If the kettle is left on for 5 minutes will it boil dry?
Cwater = 4200 J kg-1 K-1
lwater = 2260 kJ kg-1
• Energy supplied = 3000 x 5 x 60
= 9 x 105 J
• Energy required to boil the water
• = mcDq
• = 2 x 4200 x 80
• = 6.72 x 105 J
• Energy left over to change water into steam
• = (9.00 – 6.72) x 105 J
• = 2.28 x 105 J
A Level Physics
LOJ March 2004
A kettle of power 3kW holds 2 litres of water at room temperature – 20oC.
If the kettle is left on for 5 minutes will it boil dry?
Cwater = 4200 J kg-1 K-1
lwater = 2260 kJ kg-1
• Energy supplied = 3 000 x 5 x 60
= 9 x 105 J
• Energy required to boil the water
• = ml
• = 2 x 2 260 000
• = 4 520 000 J
•
•
•
•
Energy left over to change water into steam
= 228 000 J
A surplus of 228 000 – 4 520 000 = - 429000J
Therefore it would not boil dry, even then – but it would
boil!!
A Level Physics
LOJ March 2004
Summary
• You should be able to understand
what is happening to the particles in a
substance when heat is added to it or
taken away.
A Level Physics
LOJ March 2004
Summary
• If the substance is remote from its
melting or boiling point it will change
temperature (getting hotter or colder) as
the particles vibrate faster or slower on
absorbing the heat energy - the kinetic
energy component changes significantly the
potential energy component is virtually the
same..
A Level Physics
LOJ March 2004
Summary
• The amount of heat energy required to
make a temperature change of 1K will
depend on the mass of the substance
• The more you have the more energy you
will need, natch!
• It will also depend on what it is.
• Some structures react to heat input more
dramatically than others (this is indicated
in the SHC 'c' of the substance) - low 'c'
substances have particles that are easier
to 'vibrate'!
A Level Physics
LOJ March 2004
Summary
• If the substance is at its
boiling/melting point the energy
given/taken away will not be used to
get hotter or colder.
• It will be used to change state.
• If absorbed at the change of state
point (given to the substance) it will
not make the particles vibrate any
faster, but will make them freer from
each other.
A Level Physics
LOJ March 2004
Summary
• If being taken away, again it will not
change the vibration of the particles
but rather will make them more
structured - less free - and change
their state to do that.
• So when latent heat is involved we are
looking at the change of potential
energy not kinetic energy.
A Level Physics
LOJ March 2004
Summary
• You should be able to do calculations
involving heat being given and/or
taken away.
• Remember to add up all of the
components that have been 'given
energy' and all of those that have
'given energy away' and equate them
in an exchange of heat problem.
A Level Physics
LOJ March 2004
Summary
• You should be able to define specific
heat capacity and latent heat and
recall the equations.
A Level Physics
LOJ March 2004
AQA Exam Question
1.00 kg water is brought to the boil inside an electric kettle.
Throughout the heating process the heating element supplies
energy at a constant rate.
Assume that the energy supplied to the kettle itself is negligible.
a) Calculate the rate at which energy is supplied to convert water
to steam if 0.50g of steam is produced each second after the
water has reached boiling point.
b) Estimate the rate at which the temperature increases just
before the water reaches boiling point.
c) State and explain the main reason why the rate of increase in
temperature is not constant during the heating process.
A Level Physics
LOJ March 2004
Calculate the rate at which energy is supplied to convert
water to steam if 0.50g of steam is produced each
second after the water has reached boiling point.
• 0.5g water turns to steam each
second.
• l = 2260 kJ kg-1 = 2260 J g-1
• Therefore energy required to do this
is 2 260 000 x 0.5/1000 = 1 130 J
• This is supplied each second
therefore the rate is 1.13 kW
A Level Physics
LOJ March 2004
b) Estimate the rate at which the temperature increases just
before the water reaches boiling point.
• To raise 1 kg water by 1K you need
4200 J
• 1130J is supplied in a second…
• Therefore the number of degrees
Kelvin that the temperature
increases by, in that last second is:
• 1130/4200 = 0.27K
• And the rate of increase is 0.27K/s
A Level Physics
LOJ March 2004
c) State and explain the main reason why the rate of increase
in temperature is not constant during the heating process.
• Heat loss to the surroundings
depends on the temperature
difference between the hot body and
the temperature of the surroundings.
• The bigger the difference the
greater the rate at which heat loss
will occur.
A Level Physics
LOJ March 2004
AEB Question from 1984 – Typical
synoptic question.
• An X-ray tube is operating at a potential of
125 kV and 10 mA.
• (a) If only 1% of the electrical power is
converted to X-rays, at what rate is the
target being heated per second?
• (b) If the target has a mass of 0.3kg and is
made of a material with a specific heat
capacity of 150J kg-1 K-1 at what rate does
its temperature rise?
• (c) What assumption have you made in
calculating the value for part b?
A Level Physics
LOJ March 2004
(a) If only 1% of the electrical power is converted to X-rays, at what rate is the target
being heated per second?
• Energy from electrical supply per
second = power
P = IV
= 10 X 10-3 x 125 000
= 1250 W
99% used in heating = 1240W (3sf)
A Level Physics
LOJ March 2004
(b) If the target has a mass of 0.3kg and is made of a
material with a specific heat capacity of
150J kg-1 K-1 at what rate does its temperature rise?
• E = mcDq
• Each second 1240 J energy is
supplied to the anode target.
• 1240 = 0.3 x 150 x Dq
• Therefore the temperature rises at a
rate of:
Dq = 1240/(0.3 x 150)
= 27.6K per second
A Level Physics
LOJ March 2004
(c) What assumption have you made in
calculating the value for part b?
• The assumption is that there are no
thermal losses to the surroundings.
A Level Physics
LOJ March 2004