Determine the heat capacity of the calorimeter .
And to measure the calefaction of water at a
temperature of 0 C in a calorimeter due to the
action of the ambient temperature as a function of
Determine the electrical conductivity of copper
and aluminium by recording a current-voltage
Test of the Wiedmann-Franz law.
Calorimeter vessel, 500 ml
Heat conductivity rod, Cu
Temperature meter digital
Heat conductivity rod, Al
Surface temperature probe
Heat conductive paste
Glass beaker, short, 400 ml
Universal measuring amplifier
Connecting cord, 500 mm, blue
Connecting cord, 500 mm, red
Methods of Heat Transfer
Heat transfer by collective movement of
molecules within fluids.
Mass transfer takes place through diffusion
The transfer of energy to or from a body by
means of the emission or absorption of
electromagnetic radiation. It doesn't require a
3. Conduction or diffusion
Thermal conductivity is the property of the
material that indicates its ability to conduct
The thermal conductivity of this metal
is, like electrical conductivity, determined
largely by the free electrons. Suppose now
that the metal has different temperatures at
its ends. The electrons are moving slightly
faster at the hot end and slower at the cool
The faster electrons transmit energy to the
Thermal conductivity in
Metals are particularly good conductors of
heat because their particles are very
closely packed so the vibrations are
passed on very quickly. They also contain
large numbers of "free electrons".
As the metal is heated, the free electrons
source are heated.
to the heat
This makes them move faster and they
metal, colliding with both atoms and other
The heat capacity of a substance is the amount of heat required to
change its temperature by one degree, and has units of energy
Q = C dt
Q = amount of heat supplied (J)
C = heat capacity of the system or object
dt = temperature rise (K,)
The SI unit for heat capacity is J/K (joule per
Fourier’s law oF heat
If a temperature difference exists
between different locations of a
body, heat conduction occurs.
The quantity of heat dQ transported with
time dt is a
function of the cross-sectional area A and
Temperature gradient dT/dx
perpendicular to the surface.
Can find λ.
As free electrons are mainly responsible for heat conduction in
They can be considered as a Fermi gas.
They obey Fermi-Dirac distribution.
So no of particles with momentum p,
z-1 =e- βμ
μ= εF (1-π2/12(KT/ εF )2 +………)
So at T=0 and also at room temperature,
where εF = Fermi Energy
So at T=0 and room temperature,
<np>= 1/eβ(εp- εF)+1
So electronic energy can’t go beyond Fermi energy so
the electrons which are sitting below Fermi energy are
mainly responsible for conduction.
Procedure for Thermal
1.Measurement of heat capacity of lower calorimeter
The heat capacity of the calorimeter is
obtained from results of the mixing experiment
and the following formula:
cw = Specific heat capacity of water, mW =
Mass of the water, Tw = Temperature of the hot
water, T = Mixing temperature and T =
• Weigh the calorimeter at room
• Measure and record the room
temperature and the temperature of
the preheated water provided.
• After filling the calorimeter with hot
water, determine the mixing
temperature in the calorimeter.
• Reweigh the calorimeter to
2)Determination of the influence of the surroundings
The addition of heat from the
surroundings is calculated from the
(Temperature (T) rise of the cold
water in the calorimeter)
Where T0 = Temperature at time t =
Weigh the empty lower calorimeter.
Add ice to the lower calorimeter till the
temperature reaches to 0 C.
Then remove the ice and take the
temperature readings in 1 min interval till
the temperature rises to 10 C.
Reweigh the calorimeter to determine
the mass of the water that it contains.
Calefaction of cold water,
Slope of the graph gives us
3. Determination of the heat flow through metal rod thermal
Equation for the measurement of the
thermal conductivity of
Aluminium/copper rod is given by
Weigh the empty, lower calorimeter.
Insert the insulated end of the metal rod into the
upper calorimeter vessel. To improve the heat
transfer, cover the end of the metal rod with
When doing so, care must be taken to ensure
that the non-insulated end of the rod remains
completely immersed in the cold water during
Using an immersion heater, bring the water in
Keep the water in the lower calorimeter
at 0 C with the help of ice.
The measurement can be begun when
a constant temperature gradient has
become established between the upper
and lower surface probes.
At the onset of measurement, remove
the ice from the lower calorimeter.
Measure and record the change in the
differential temperature and the
temperature of the water in the lower
calorimeter for a period of 5 minutes.
Temp of lower
Slope of the graph gives,
Since at steady state,
We can find λ using Fourier's
the current through a conductor
directly proportional to the potential
difference across the two points.
Here the constant for proportionality
is R, is the Resistance.
Resistance can also be defined as,
R=ρL / A
ρ = Resistivity
A = Cross sectional area
The inverse of resistivity is called
σ = 1/ρ,
Experimental Setup for Electrical conductivity measurement
Measurement of the electrical conductivity.
This is the Circuit diagram for the
measurement of Electrical Conductivity.
according to the circuit
Adjust amplifier and voltage in variable
transformer described as
Set the rheostat to its maximum value and
the value during the experiment.
From the graph,
Slope will give us R
So Electrical conductivity,
σ= l / AR;
At a given temperature, the thermal and
electrical conductivities of metals are
proportional, but raising the temperature
increases the thermal conductivity while
decreasing the electrical conductivity. This
behaviour is quantified in the WiedemannFranz Law.
λ / σ = LT or L= λ / σT
Heat Capacity of Calorimeter = 85.23 J/K
Thermal conductivity of Aluminium =315.56 Wm-1K-1
Literature value = 205 Wm-1K-1
Thermal conductivity of Copper =952.94 Wm-1K-1
Literature value = 386 Wm-1K-1
Electrical conductivity of Aluminium =3.651*107 Ω-1m-1
Literature value = 3.75*107 Ω-1m-1
Electrical conductivity of Copper =5.764*107 Ω-1m-1
Literature value = 5.882*107 Ω-1m-1
PRECAUTIONS & Discussion
Care should be taken to ensure the
immersion heater used is not exposed to
air for long.
Always maintain minimum water level
in the upper calorimeter while
maintaining at 100 C.
Handle temperature probes with care.
Bending front portion too much damage
Obtained values for electrical
conductivity are very close to the
literature values. But for thermal
conductivity it is significantly different.
This is because,
It is very difficult to obtain a constant
temperature gradient since we have to
keep both the calorimeter in fixed
Even though after coming to steady
state the system will get disturbed due
Suhas K Ramesh