1. 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.
2. 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
3. THERMAL CONDUCTIVITY ESTIMATION
4. 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
5. 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
6. 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.
7. 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).
8. Fouriers 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 .
9. 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,
=1/[z-1ep ]+1 z-1 =e- =1/[e(p-) ]+1 = F (1-2/12(KT/ F )2 +) So at
T=0 and also at room temperature, =F where F = Fermi Energy So at
T=0 and room temperature, = 1/e(p- F)+1 So electronic energy cant
go beyond Fermi energy so the electrons which are sitting below
Fermi energy are mainly responsible for conduction.
10. Experimental set-up for thermal conductivity.
11. 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 =
12. 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
13. 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) Q=(cwmw+C)(T-T0) Where T0 = Temperature at time t = 0
sec.
14. 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.
15. Sample reading Calefaction of cold water, Time(min)
Temperature(0C) Qsurr(J) 1 1 0 2 1.2 294.3 3 1.3 515.2 Slope of the
graph gives us dQsurr/dt
16. 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
17. 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
18. 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.
19. Sample Calculation Time(s) Temp of lower calorimeter(0C)
T(0C) Q(J) 0 3 30.57 0 20 3.2 30.48 190.6 40 3.3 30.32 270.8
Q=(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=T/ x
We can find using Fourier's conduction formula.
20. Electrical Conductivity Estimation
21. ohms 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
22. Conductivity Resistance can also be defined as, R=L / A
Where, = Resistivity L= Length A = Cross sectional area The inverse
of resistivity is called Conductivity. Electrical conductivity =
1/,
23. Experimental Setup for Electrical conductivity
measurement
24. Measurement of the electrical conductivity. This is the
Circuit diagram for the measurement of Electrical
Conductivity.
25. 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.
26. 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, = l / AR;
27. Relation between electrical and thermal
conductivity???
28. 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. / = LT or L= / T where,
29. 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
-1m-1 Literature value = 3.75*107 -1m-1 Electrical conductivity of
Copper =5.764*107 -1m-1 Literature value = 5.882*107 -1m-1
30. 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
31. 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
32. Presented by, Suhas K Ramesh Rollno-10094 IISER BHOPAL