The document describes procedures to determine the heat capacity of a calorimeter, measure the heating of water due to ambient temperature, and estimate the thermal and electrical conductivity of copper and aluminum. To measure thermal conductivity, the experiment determines the heat flow through metal rods using temperature measurements and Fourier's law of heat conduction. Electrical conductivity is estimated by recording current-voltage characteristics and calculating resistivity from Ohm's law. Results are found to be close to literature values. The Wiedemann-Franz law relating thermal and electrical conductivity is also discussed.

2. OBJECTIVES
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
time.
Determine the electrical conductivity of copper
and aluminium by recording a current-voltage
characteristic line.
Test of the Wiedmann-Franz law.

3. APPARATUS
 Calorimeter vessel, 500 ml
Immersion heater
 Heat conductivity rod, Cu
Temperature meter digital
 Heat conductivity rod, Al
Temperature probe
 Magnetic stirrer
Surface temperature probe
 Heat conductive paste
Stopwatch
 Gauze bag
Supporting block
 Rheostat
Glass beaker, short, 400 ml
Universal measuring amplifier
Digital multimeter
Connecting cord, 500 mm, blue
Connecting cord, 500 mm, red

4. THERMAL
CONDUCTIVITY
ESTIMATION

5. Methods of Heat Transfer
1. Convection
Heat transfer by collective movement of
molecules within fluids.
Mass transfer takes place through diffusion
2. Radiation
The transfer of energy to or from a body by
means of the emission or absorption of
electromagnetic radiation. It doesn't require a
medium.
3. Conduction or diffusion

6. Thermal conductivity
Thermal conductivity is the property of the
material that indicates its ability to conduct
heat.
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
end.
The faster electrons transmit energy to the

7. Thermal conductivity in
metals
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
closest
source are heated.
to the heat
This makes them move faster and they
travel
through the
metal, colliding with both atoms and other
electrons.

8. Heat capacity
The heat capacity of a substance is the amount of heat required to
change its temperature by one degree, and has units of energy
per degree
Q = C dt
where
Q = amount of heat supplied (J)
C = heat capacity of the system or object
(J/K)
dt = temperature rise (K,)
The SI unit for heat capacity is J/K (joule per
kelvin).

9. Fourier’s law oF heat
conduction
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
the
Temperature gradient dT/dx
perpendicular to the surface.
i.e.,
Can find λ.

10. As free electrons are mainly responsible for heat conduction in
metals,
They can be considered as a Fermi gas.
They obey Fermi-Dirac distribution.
So no of particles with momentum p,
<np>=1/[z-1eβεp ]+1
z-1 =e- βμ
=1/[eβ(εp-μ) ]+1
μ= εF (1-π2/12(KT/ εF )2 +………)
So at T=0 and also at room temperature,
μ=εF
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.

11. Experimental set-up for thermal conductivity.

12. Procedure for Thermal
conductivity estimation
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 =

13. procedure
• Weigh the calorimeter at room
temperature.
• 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

14. 2)Determination of the influence of the surroundings
The addition of heat from the
surroundings is calculated from the
temperature increase
(Temperature (T) rise of the cold
water in the calorimeter)
ΔQ=(cwmw+C)(T-T0)
Where T0 = Temperature at time t =
0 sec.

15. procedure
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.

16. Sample reading
Calefaction of cold water,
Time(min)
Temperature(0C)
ΔQsurr(J)
1
1
0
2
1.2
294.3
3
1.3
515.2
Slope of the graph gives us
dQsurr/dt

17. 3. Determination of the heat flow through metal rod thermal
conductivity
Equation for the measurement of the
thermal conductivity of
Aluminium/copper rod is given by

18. Procedure
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
heat-conduction paste.
 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
the experiment.
Using an immersion heater, bring the water in

19. 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.

20. Sample Calculation
Time(s)
Temp of lower
calorimeter(0C)
ΔT(0C)
ΔQ(J)
0
3
30.57
0
20
3.2
30.48
190.6
40
3.3
30.32
270.8
ΔQ=(cwmw+C)(T-T0)
Slope of the graph gives,
dQtotal/dt.
So (dQ/dt)rod=(dQ/dt)tot-(dQ/dt)surr
Since at steady state,
dT/dx=ΔT/ Δx
We can find λ using Fourier's
conduction formula.

21. Electrical
Conductivity
Estimation

22. ohm’s law
Ohm's
law
states
that
the current through a conductor
between
two
points
is
directly proportional to the potential
difference across the two points.
Here the constant for proportionality
is R, is the Resistance.
V=I R

23. Conductivity
Resistance can also be defined as,
R=ρL / A
Where,
ρ = Resistivity
L=
Length
A = Cross sectional area
The inverse of resistivity is called
Conductivity.
Electrical conductivity
σ = 1/ρ,

24. Experimental Setup for Electrical conductivity measurement

25. Measurement of the electrical conductivity.
This is the Circuit diagram for the
measurement of Electrical Conductivity.

26. Procedure
Perform
the
experimental
set-up
according to the circuit
diagram.
Adjust amplifier and voltage in variable
transformer described as
in the
manual.
Set the rheostat to its maximum value and
slowly decrease
the value during the experiment.

27. Sample reading
For copper,
Voltage(mV)
Current(mA)
2.3
0.40
3.6
0.45
8.9
0.50
From the graph,
Slope will give us R
So Electrical conductivity,
σ= l / AR;

28. Relation between
electrical
and
thermal
conductivity???

29. Wiedemann-Franz law
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
where,

30. Results
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

31. 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

32. 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
temperatures.
Even though after coming to steady
state the system will get disturbed due

33. Presented by,
Suhas K Ramesh
Rollno-10094
IISER BHOPAL

34. Links
•http://www.engineeringtoolbox.com/heat-capacity-d_338.html
•http://www.chm.davidson.edu/vce/calorimetry/heatcapacity.html
•http://www.ndted.org/EducationResources/CommunityCollege/Materials/Physical_Chemi
cal/ThermalConductivity.htm
•http://www.eos.ubc.ca/ubcgif/iag/foundations/properties/resistivity.htm