10/11/24, 2:12 PM Thermo Couple-Seebeck Effect (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa

ita Vishwa Vidyapee…

Thermo Couple-Seebeck Effect

Aim:
To verify the relation between thermo emf of a thermocouple and temperature difference between two hot junctions.

Theory:
The conversion of temperature difference to electric current and vice-versa is termed as thermoelectric effect. In 1981, Thomas Johann
Seebeck found that a circuit with two dissimilar metals with different temperature junctions would deflect a compass magnet. He realised
that there was an induced electric current, which by Ampere's law deflect the magnet. Also electric potential or voltage due to the
temperature difference can drive the electric current in the closed circuit.
To measure this voltage, one must use a second conductor material which generates a different voltage under the same temperature
gradient. Otherwise, if the same material is used for measurement, the voltage generated by the measuring conductor would simply cancel
that of the first conductor. The voltage difference generated by the two materials can then be measured and related to the corresponding
temperature gradient. It is thus clear that, based on Seebeck's principle; thermocouples can only measure temperature differences and need
a known reference temperature to yield the absolute readings.
The principle behind it states that

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V- Voltage difference between two dissimilar metals

a- Seebeck coefficient
Th - Tc - Temperature difference between hot and cold junctions

There are three major effects involved in a thermocouple circuit: the Seebeck, Peltier, and Thomson effects.
The Seebeck effect describes the voltage or electromotive force (EMF) induced by the temperature difference (gradient) along the wire. The
change in material EMF with respect to a change in temperature is called the Seebeck coefficient or thermoelectric sensitivity. This
coefficient is usually a nonlinear function of temperature.

Peltier effect describes the temperature difference generated by EMF and is the reverse of Seebeck effect. Finally, the Thomson effect
relates the reversible thermal gradient and EMF in a homogeneous conductor. Thermocouples generate an open-circuit voltage, called the
Seebeck voltage that is proportional to the temperature difference between the hot and reference junctions:

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Since thermocouple voltage is a function of the temperature difference between junctions, it is necessary to know both voltage and reference
junction temperature in order to determine the temperature at the hot junction. Consequently, a thermocouple measurement system must
either measure the reference junction temperature or control it to maintain it at a fixed, known temperature.

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10/11/24, 1:49 PM Heat transfer by Conduction (Simulator) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeet…
Temperature of main heater Temperature of cold plat
Material Voltmeter V(V) Ammeter I(A) Diameter d(cm) Area of specimen,A(m2) Thickness,Δx(cm)
T1 o C T2 o C T3 o C T4 o C mean ThoC T5oC T6 o C mean TcoC
cardboard 110 0.31 10 0.007850000000000001 0.5 26.59 25.78 25.6 25.78 25.9375 0 0 0
glass 120 0.4 10 0.007850000000000001 0.5 6.6 6.9 6.04 6.95 6.6225 0 0 0
mica 130 0.48 10 0.007850000000000001 0.5 13.05 13.9 13.9 13.9 13.6875 0 0 0
asbestoes 140 0.54 10 0.007850000000000001 0.5 16.11 16.27 15.45 16.27 16.025 0 0 0
ebonite 0 0 0 0 0 0 0 0 0 0 0

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10/11/24, 1:45 PM Heat transfer by Conduction (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

Heat transfer by Conduction

Aim:

1. To find the thermal conductivity of a material by the two slabs guarded hot plate method.
2. To find the thermal resistance of the sample.

Apparatus:
A circular main heater plate (MH) is surrounded by an annular guard heater plate (GH) with a
narrow air gap in between. Each heater is made up of electrical resistance wire sandwiched
between two copper plates. Thermocouples are fixed to the plates to measure their surface
temperatures.
Two identical circular slabs of the material to be tested are placed on either side of and in good
thermal contact with the heater plates. On the outer sides of the two slabs, in good thermal
contact, are two circular water-cooled slabs whose surface temperatures can also be monitored
with thermocouples (Fig 1).
The purpose of the guard heater is to prevent heat loss from the edge of the main heater by maintaining the temperature outside the main
heater at the same temperature as the main heater. This ensures that all heat lost from the main heater flows through the test slabs.

Theory:

The theory of heat transfer seeks to predict the energy transfer that may take place between material bodies as a result of temperature
difference. This energy transfer is defined as heat. The three modes by which heat can be transferred from one place to another are
conduction, convection and radiation.
In conduction, heat is carried by means of collisions between rapidly moving molecules closer to the hot end of a body of matter and the
slower molecules closer to the cold end. Some of the kinetic energy of the fast molecules passes to the slow molecules, and as a result of
successive collisions, heat flows through the body of matter from the hot end to the cold end. Solids, liquids, and gases all conduct heat.
Conduction is poorest in gases because their molecules are relatively far apart and so interact less frequently than in solids and liquids.
Metals are the best conductors of heat because some of their electrons are able to move about relatively freely and can interact frequently by
collisions.
Without the guard heater, cooler air surrounding the edge of the main heater would be heated by conduction and convection. Thus some of
the heat supplied to the main heater would be carried away by the surrounding air.
With the guard heater in place and adjusted to the same temperature as the main heater, the air in the gap between is maintained at the
temperature of the main heater, so no heat is lost at the edge of the main heater. All heat lost from the main heater must flow into the test
slabs.

Consider one dimensional heat conduction (Fig 2). The rate at which heat is conducted through a slab of a particular material is proportional
to the area A of the slab and to the temperature difference ΔT between its sides and inversely proportional to the slab's
thickness d.

The amount of heat Q that flows through the slab in the time t is given by

Rate of conduction

And thus (1)

Where ΔT = T1 – T2, and k is the thermal conductivity of the

material, is a measure of its ability to conduct heat. The SI unit of k is Wm-1K-1.

Thermal conductivity: Note that a heat flow rate is involved, and the numerical value of the thermal conductivity indicates how fast heat will
flow. In general, thermal conductivity is strongly temperature dependent. It has the units of watts per meter per Kelvin. Heat transfer by
conduction in a solid can be realized through the support of phonons, electrons and photons. The individual contributions of these carriers
widely depend on material and its temperature. Thermal conductivity is thus a second order tensor, but in a material with cubic isotropy it
reduces to a scalar. It is an intensive property (changing the amount of material does not change its thermal conductivity) and is a function
of both pressure and temperature.
The thermal resistance R of a layer of a material of thickness d and of thermal conductivity k is given by

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10/11/24, 1:45 PM Heat transfer by Conduction (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

Heat transfer by Conduction

. (2)

The greater the value of R, the greater the resistance to the flow of heat.

Applications:
Heat transfer has wide applications for the proper functioning of thermal devices and systems. This principle is used to solve many problems
in thermal mechanics.

1. Heat exchangers.
2. Building construction works.
3. Thermal energy storage devices.
4. Heat transfer in human body.
5. Thermopile and infrared thermometer.
6. Thermal resistance in electronics like thermal diode or thermal rectifier.
7. Used in laser cooling, radiative cooling, magnetic cooling, etc.

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10/11/24, 1:54 PM Heat Transfer by Natural Convection (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidy…

Heat Transfer by Natural Convection

Aim:
Heat Transfer by Natural Convection

1. To determine the overall heat transfer coefficient at the surface of a given vertical metal
cylinder by the natural convection method.
2. To determine the value of Nusselt number.

Apparatus:
Natural Convection Apparatus - a metal cylinder fitted
vertically in a wooden rectangular duct which is open at the
top and the bottom (Fig 1). An electric heater is provided in
the vertical cylinder, which heats the surface of the cylinder.
Heat is lost from the cylinder to the surrounding air by
natural convection, because the air in contact with the
cylinder gets heated and becomes less dense, causing it to
rise. This in turn creates a continuous flow of air upward in
the duct. The temperature at the various locations on the
surface of the vertical cylinder and in the incoming and
outgoing air is monitored with thermocouples. The duct is
made of wood because it is a poor conductor, so not much
heat will transfer from the air to the duct. Thus the duct will
enhance air flow without introducing another convective
surface.

Theory:

Heat transfer theory seeks to predict the energy transfer that takes place between material bodies as a result of temperature difference. This
energy transfer is defined as heat. The three modes by which heat can be transferred from one place to another are conduction, convection
and radiation.
It is well known that a hot plate of metal will cool faster when placed in front of a fan than when placed in still air. With the fan, we say that
the heat is convected away, and we call the process convection heat transfer. Convection involves the transfer of heat by motion and mixing
of a fluid.
Forced convection happens when the fluid is kept in motion by an external means, such as a turbine or a fan. Some examples of forced
convection are stirring a mixture of ice and water, blowing on the surface of coffee in a cup, orienting a car radiator to face airflow, etc.
Convection is called natural convection when motion and mixing of fluid is caused by density variation resulting from temperature differences
within the fluid. The density of fluid near the hot surface is less than that of the colder fluid away from the heated surface, and gravity
creates a buoyant force which lifts the heated fluid upward.

In the case of conduction through a solid of area A and thickness L, heat flow is given by

(1)

Where ∆T is the temperature difference across the thickness L, and k is the thermal conductivity of the object.

In the case of convection, the heat flow is proportional only to the surface area A of the object,

(2)

Where h is the convective heat transfer coefficient (units Wm-2 K-1) which depends on the shape and orientation of the object.
∆T is the temperature difference between the surface of the object and the surrounding fluid.

Convection is an enhanced form of conduction, since the movement of the fluid helps carry heat transferred by conduction, so one would
expect some relation between h and k. If the temperature of the cylinder is not much above that of the surrounding air, the moving fluid can
be approximated as a stationary layer having some characteristic thickness L. Comparing equations (1) and (2), one immediately has the
relation h = k/L. In fact, as the temperature of the cylinder increases, fluid motion increases and becomes turbulent, whereupon the fluid
becomes more efficient at carrying heat, and h can turn out to be 102 – 104 times k/L.The proportionality between h
and k/L is called the Nusselt number N,

(4)

Where k is thermal conductivity of air and L is the characteristic length. Note that N is a dimensionless quantity.

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10/11/24, 1:54 PM Heat Transfer by Natural Convection (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidy…

In our case, which does involve turbulent flow, we are interested in temperature variation along the length of a metal cylinder, so we will take
the characteristic length L to be the length of the cylinder.
Applications:
Natural convection heat transfer is extensively used in the following areas of engineering:
1. Cooling of commercial high voltage electrical power transformers.
2. Heating of houses by electrical baseboard heaters.
3. Heat loss from steam pipe lines in power plants and heat gain in refrigerant pipe lines in air conditioning applications.
4. Cooling of reactor cores in nuclear power plants, though often the coolant is driven by pumps, resulting in more efficient heat transfer by
forced convection.
5. Cooling of electronic devices (chips, transistors) by finned heat sinks, though a fan is often present to augment the natural convection with
forced convection.

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10/11/24, 2:01 PM Heat Transfer by Radiation (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeet…

Heat Transfer by Radiation

Procedure:
Variable Region:
1. Choose material - This can be used to select the specimen plate.
2. Diameter of the specimen- Used to vary the diameter of the specimen in centimeter.
3. Thickness of the specimen- Used to change the thickness of the specimen in centimeter.
4. Chamber temperature- This is used to change the temperature in the evacuated chamber in degree Celsius.

Measurement Region:
White knobs in simulator- This knob can be rotated by right clicking side arrows and thereby adjusting the voltage and corresponding
current which is given as input power.
Tuning Switch- Used to turn either Black plate (BP) or Test plate (TP) and thereby can change the corresponding voltage and current for
both the plates.
Note: Power should be given for both the plates must be same.
Power on button- Using this button we can switch on the power when all the initial adjustments were done.
Temperature indicator in the simulator- After steady state of temperature is reached (20 minutes in timer). Adjusting the knob by
clicking the side arrows in the indicator, thereby T1 to T7 temperature on thermocouples can be noted in degree Celsius.

Procedure for Simulation

1. Choose a particular material to perform simulation.
2. Fix the value of diameter and thickness of the plate.
3. The temperature is given to the chamber using the slider " chamber temperature".
4. Using tuning switch and white knob, fix the voltage and corresponding current for black plate and test plate.
5. Note the value of temperature T1, T2, T3,T4,T5,T6,T7 using temperature indicator.
6. Calculate the value of emissivity for a given test plate using equations.

Procedure for Real lab

Using emissivity apparatus, the power is given to carry out the experiment using voltmeter and ammeter. After steady state is reached,(2
hours), Using stop watch, every half an hour, the temperature in the temperature indicator is noted. Using trial and error method, T1,T2, T3,
T4, T5, T6, and T7 are noted. Calculate the value of emissivity for a given test plate using equations.

Observations and Calculations:

Heat emitted by the black body,

Heat emitted by the test plate,

εb Emissivity of the black plate and it is equal to 1

εp Emissivity of the test plate

σ Stefan-Boltzmann constant = 5.67×10-8 W m-2K-4

=..........................K

= ...................K

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10/11/24, 2:01 PM Heat Transfer by Radiation (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeet…

Qb = Qp since input power to the two plates is same and conduction heat loss are also same.

Emissivity of the specimen plate,

Result
Emissivity of test plate surface =

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10/11/24, 2:00 PM Heat Transfer by Natural Convection (Simulator) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vi…

Heat Transfer by Natural Convection

emperature of the air

o
T 6o C mean Heat transfer co efficient h(Wm-2K-1) Nusselt Number N
1 C
0 36 33 -68.222538509491 -1563.433174175…
0 36 33 8.207858896645742 188.09676638146…
0 36 33 8.207858896645742 188.09676638146…
0 36 33 7.109803393427123 162.93299443270…
0 36 33 5.250220988869025 120.31756432824…

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10/11/24, 2:00 PM Heat Transfer by Radiation (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetham…

Heat Transfer by Radiation

Aim:
Heat Transfer by Radiation

1. To compare heat transfer between different material surface and the black body surface by
radiation.
2. To find the emissivity of different material surface.

Apparatus:
Emissivity measurement apparatus: The experimental set up consists of two circular aluminum
plates identical in size provide with heater coils at the bottom Fig.1

It is kept in an enclosure so as to provide undisturbed natural convection surroundings. The

heat input to the heaters is varied by two regulators and is measured by an ammeter and
voltmeter. Each plate is having three thermocouples; hence an average temperature is
taken. One thermocouple is kept in the enclosure to read the chamber temperature. One
plate is blackened by a layer of enamel black paint to form the idealized black surface
whereas the other plate is the test plate. The temperatures of the plates are measured by
using thermocouples.

Theory:
In radiation, energy is carried by the electromagnetic waves emitted by every object. In general, radiation is a volumetric phenomenon. This
is because the electrons, atoms and molecules of all solids, liquids and gases above absolute zero temperature are in constant motion and
hence energy is constantly emitted, absorbed and transmitted throughout the entire volume of the matter.

The radiation from a surface is emitted in all possible directions. A body at a temperature above absolute zero emits radiation in all directions
over a wide range of wavelength. The amount of radiation from the surface of a body at a given temperature and at a given wavelength
depends on the material of the body and nature of its surface. A concept of an idealized surface has been made which are perfect emitter and
absorber of radiation. This ideal surface is known as a black body.
A black body or ideal radiator is a body that emits and absorbs at any temperature the maximum possible radiation at any given wavelength.
A black body has the following features

1. At a specified temperature and wavelength a black body emits more radiation energy than the real one.
2. It absorbs all incident radiation regardless of wavelength and direction
3. It emits radiation energy uniformly in all direction. That is black body is a diffuse emitter the term
‘diffuse’ means independent of direction.

Depending on type of surface, the reflected radiation is specular or

diffuse. A smooth and polished surface is more specular while the rough
surface is more diffuse.

The fraction of incident energy absorbed by the surface is called the

absorptivity. For a black body it is equal to one.

Actually black body do not exist in nature through its characteristics are
approximated by a hole in a box filled with highly absorptive material.
The emission spectrum of such a black body was first fully described by
Max Planck.

Emissivity of a surface is defined as ratio of the radiation emitted by the

surface to the radiation emitted by the black body at the same temperature.

If a sample is replaced by a black body of temperature of same area at same temperature, under thermal equilibrium, the emissivity of the
body is equal to the absorptivity.

Relationship between Absorptivity and Emissivity:

Consider two flat infinite plates, surface A and surface B, both emitting radiation towards one another.
Surface B is assumed to be an ideal emitter, εB= 1.

Surface A will emit radiation according to Stefan’s Boltzmann law as

(1)

And will receive radiation as

(2)

Net heat flow from surface A will be

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10/11/24, 2:00 PM Heat Transfer by Radiation (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetham…

(3)

Now suppose that the two surfaces are at exactly same temperature then, εA = αA
Emissivity of surface will depend on the material of which it is composed.
The radiation emitted per unit area per unit time from the surface of a body is called its emissive power. The ratio of emissive power of a
body to the emissive power of a black body is called emissivity.

Heat emitted by the black body per unit area, (4)

Heat emitted by the test plate per unit area, (5)

εb Emissivity of the black plate.

εp Emissivity of the test plate

σ Stefan-Boltzmann constant = 5.67×10-8 W m-2K-4

Tb Black body temperature in Kelvin
Tc Chamber temperature in Kelvin
Tp Test plate temperature in Kelvin
Qb = Qp since input power to the two plates is same and conduction heat loss are also same.

Emissivity, (6)

Working

The same amount of power input is given to both test plate and black plate. After achieving steady state temperature for black plate, it
continuously emits radiations and this radiation is completely absorbed by the test plate. But its emit radiation is slightly less than the black
body because emissivity depends on nature of the material.

Applications
1. In lasers
2. Microwave ovens
3. Solariums
4. Mobile telephones
5. MRI devices in the magnetic field
6. Industrial heaters

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10/11/24, 2:11 PM The Study of Phase Change (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

The Study of Phase Change

Aim:
To study the phase change of a substance from liquid to solid by plotting the cooling curve.
To determine the melting point of the given substance and to find out the transition time.

Theory:
The term change of phase means the same thing as the term change of state. The change of phase always occurs with a change of heat.
However the temperature does not change. When we heat a solid, the energy supplied is used to increase the kinetic energy of its molecules,
and thereby its temperature increases. Energy is required to melt a solid, because the cohesive forces between molecules must be partially
overcome to allow the molecules to move about. Similarly, energy is required to vaporize a liquid, because in so doing the molecules are
separated and molecular attractive forces are overcome. But there is no temperature change until a phase change is complete. i.e. during
phase change, the energy supplied is used only to separate the molecules ; no part of it is used to increase the kinetic energy of the
molecules. So its temperature will not rise, since kinetic energy of molecules remains the same.

The quantity of heat absorbed or released when a substance changes its physical phase at constant temperature (e g. From solid to liquid at
melting point or from liquid to gas at boiling point) is termed as its latent heat. The quantity of heat absorbed or released when unit mass of
a substance changes its physical phase at a given temperature is called specific latent heat. The constant temperature at which melting or
boiling take place is known as the melting or boiling point.

The process, phase transition is governed by Newton's law of cooling, which states that,
" the rate of change of temperature of an object is proportional to the difference between its own temperature and the temperature of its
surroundings."

i.e,

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,
where , T is the temperature of the object
k is a positive constant
Tais the temperature of the surroundings.

By studying the phase change of a substance from solid to liquid, one can determine the melting point, latent heat of fusion etc of the
substance.

In order to understand more about the theory of phase change, consider a sample cooling curve for a substance with a melting point of
450 C.
The flat portion of the graph represents the phase change from liquid to solid at the constant melting temperature 450 C. The two curved
portions represent cooling of the liquid plus the tube (left) and cooling of the solid plus the tube (right). These cool according to Newton’s law
of cooling,

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10/11/24, 2:11 PM The Study of Phase Change (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

where T is the temperature of the sample, T0 is room temperature, and

k is a positive constant.

The heat loss rate of the liquid plus the boiling tube is likely to be the
same as the heat loss rate of the solid plus the tube for a given
temperature difference (T-T0)

The specific heat C2 of the material undergoing phase change is, however, unlikely to be the same for the liquid and the solid phases.
Thus we have

and

where upon it can be seen that the cooling constants in the liquid (l) and solid (s) phases are related by the equation

These cooling constants can be estimated by using the graph to estimate the time te taken for the material plus the tube to cool to 1/e of
their starting temperature above room temperature. Then since the solution to the Newton’s law of cooling differential equation is

we have k = 1/ te.

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10/11/24, 1:46 PM Heat transfer by Conduction (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapee…

Heat transfer by Conduction

Performing Simulation:
Simulator Controls

1. The Choose Material combo box is used to select the material for the test slab.
2. The Diameter of the material slider is used set the diameter of the portion of the test slab in contact with the main heater, in cm
3. The Thickness of material slider is used to set the thickness of the test slab, in cm.
4. The Coldwater temperature slider is used to set the temperature ( in degrees Celsius) of the water flowing inside the outer plates.
5. The White knobs in simulator can be rotated by clicking side arrows to adjust the voltage and corresponding current, which can be used
to calculate input power.
6. The MH-GH Switch is used to set either main heater (MH) or guard heater (GH) voltage and current as shown on the meters. Note: For
the simulator to be powered on, the voltage for both heaters must be the same.
7. The Power on button switches on the power after the initial adjustments are done.
8. The Temperature indicator is used to read the temperature at the positions of the various thermocouples. After a steady state is
reached (when the timer shows 20 minutes), click the arrows on either side of the knob to read temperatures T1 to T8 in degrees Celsius.

Procedure for Simulation

1. Choose the material from combo box.

2. Using the sliders, fix a particular diameter for the portion of the test slab in contact with the main heater, and a thickness for the entire
slab.
3. Adjust the cold water temperature using the slider.
4. Using the white knobs, fix the value of same voltage and current for both main heater (MH) and guard heater (GH). With the MH-GH
switch set to MH, use white MH knob to set the voltage and current for the main heater. Then click the MH-GH switch to GH and use the
white GH knob to set the voltage and current for the guard heater to the same values you set for the main heater.
5. Click the Power On switch to power the unit on.
6. After a steady state is reached (20 minutes in the timer), use the temperature indicator to read and note down T1, T2, T3, T4, T5, T6, T7
and T8.
7. Using the work sheet and the equations from the theory page, calculate the thermal conductivity of the test slab. Note: since the main
heater is in contact with a test slab on both sides, the area A in equation

(1)

where d is the diameter of the MH, not , as might first be assumed.

Procedure for Real lab

The procedure for the real lab is quite similar. The main differences are (1) the guard heater can be set to a slightly different temperature, as
needed, to keep the temperature of the main heater uniform, and (2) the calculations can be extended to allow for and/or find the
dependence of k on ΔT.

Observations and Calculations

Mean temperature at the surface of the specimen on the heater side,

= °C

Mean temperature at the surface of the specimen on cold plate side,

= °C

Area of heat transfer,

= m2

In above equation, d is the diameter of the specimen

Heat transferred,

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10/11/24, 1:46 PM Heat transfer by Conduction (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapee…

Heat transfer by Conduction

Δx is the thickness of the specimen

Thermal conductivity k= Wm-1K-1

Result:

Thermal conductivity of the given specimen by conduction = Wm-1K-1

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10/11/24, 1:54 PM Heat Transfer by Natural Convection (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa V…

Heat Transfer by Natural Convection

Performing the Simulation:

Simulator Controls

1. Choose material - This can used to select the material for the metal cylinder.
2. Side of wooden box - Side of the outer wooden hollow rectangular box can be varied in cm.
3. Height of wooden box - Height of the outer wooden hollow rectangular box can be varied in cm.
4. Diameter of cylinder- Diameter of the vertical cylinder can be varied in cm.
5. Length of the cylinder - Length of the vertical cylinder can be varied in cm.
6. Thickness of cylinder - Thickness of the vertical cylinder can be varied in cm.
7. White knob - can be rotated by clicking the side arrows to adjust the voltage and corresponding current, which can be used to calculate
input power.
8. Power On - click to start the experiment.
9. Temperature indicator - used to read the temperature at the positions of the various thermocouples. After a steady state is reached
(when the timer shows 20 minutes), click the arrows on either side of the knob to read temperatures T1 to T6 in degrees Celsius.

Procedure for Simulation

1. Choose a particular material to carry out the experiment.
2. Choose the height and side of the wooden box with the box sliders.
3. Adjust the diameter, length and thickness of the cylinder using the cylinder sliders.
4. Apply a particular voltage and corresponding current using white knob in the simulator.
5. Using temperature indicator, note the values of T1, T2, T3, T4, T5 and T6 and, using the table and worksheet below, calculate the heat
transfer coefficient and Nusselt number.
6. Click show result to check your calculations. You can also enter your data in the worksheet on the Simulator to check some of the
intermediate quantities in the main calculations.

Procedure for Real lab

The procedure for a real lab is quite similar, except that the calculations can be extended to include heat loss from the cylinder by radiation,
which is often not negligible. For example, at the highest temperatures seen in our simulation, the radiation heat loss would be comparable
to the convection heat loss, so only about half the electrical power input would be lost by convection.

Calculations and Observations:

Power input to the heater,

………………….. W

Area of heat transfer,

……………….. m2

∆T = Average temperature of the tube – Average

temperature of the air

……………. °C

We have , and by definition

=...........................Wm-2K-1

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10/11/24, 1:54 PM Heat Transfer by Natural Convection (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa V…
and

= ..............................

Where k = 0.024 Wm-1K-1 is the thermal conductivity of air, and L is the length of the cylinder, set by the slider (be sure to convert cm to
meters).

Result
Heat transfer coefficient h =……………….
Wm-2 K-1
Nusselt number N = .....................

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10/11/24, 2:08 PM Newton's Law of Cooling (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetham V…

Newton's Law of Cooling

Aim
1. The aim of the experiment is to verify Newton's Law of Cooling of different materials and
different liquids.
2. To draw the cooling curve.

Theory

Temperature difference in any situation results from energy flow into a system or energy flow from a system to surroundings. The former
leads to heating, whereas latter leads to cooling of an object.
Newton’s Law of Cooling states that the rate of temperature of the body is proportional to the difference between the
temperature of the body and that of the surrounding medium. This statement leads to the classic equation of exponential decline over time
which can be applied to many phenomena in science and engineering, including the discharge of a capacitor and the decay in radioactivity.
Newton's Law of Cooling is useful for studying water heating because it can tell us how fast the hot water in pipes cools off. A practical
application is that it can tell us how fast a water heater cools down if you turn off the breaker when you go on vacation.
Suppose that a body with initial temperature T1°C, is allowed to cool in air which is maintained at a constant temperature
T2°C.
Let the temperature of the body be T°C at time t.
Then by Newton’s Law of Cooling,

(1)

Where k is a positive proportionality constant. Since the temperature of the body is higher than the temperature of the surroundings then T-
T2 is positive. Also the temperature of the body is decreasing i.e. it is cooling down and rate of change of temperature is negative.

The constant ‘k’ depends upon the surface properties of the material being cooled.
Initial condition is given by T=T1 at t=0
Solving (1)

(2)

Applying initial conditions;

Substituting the value of C in equation (2) gives

This equation represents Newton’s law of cooling.

If k <0, lim t --> ∞, e-kt = 0 and T= T2 ,

Or we can say that the temperature of the body approaches that of its surroundings as time goes.

The graph drawn between the temperature of the body and time is known as cooling curve. The slope of the tangent to the curve at any
point gives the rate of fall of temperature.

In general,

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10/11/24, 2:08 PM Newton's Law of Cooling (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetham V…
where,

T(t) = Temperature at time t,

TA = Ambient temperature (temp of surroundings),
TH = Temperature of hot object at time 0,
k = positive constant and
t = time.

Example of Newton's Law of Cooling:

This kind of cooling data can be measured and plotted and the results can be used to compute the unknown parameter k. The parameter can
sometimes also be derived mathematically.

Applications

1. To predict how long it takes for a hot object to cool down at a certain temperature.
2. To find the temperature of a soda placed in a refrigerator by a certain amount of time.
3. It helps to indicate the time of death given the probable body temperature at the time of death and current body temperature.

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10/11/24, 2:08 PM Newton's Law of Cooling (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

Newton's Law of Cooling

Performing the Simulation:

This is the experimental set up that the user can see on the simulator.

User Instructions
The simulator consists of three regions:

1. Simulator’s viewable window.

2. Variable menu.
3. Measurement menu.

Variable Menu:
The variable menu contains two drop down combo boxes and two buttons. The user can select the desired material and liquid from these
combo boxes. Here select the material (say 'Brass') and liquid (say 'Water'), then click on the Start Heating button. The temperature starts
rising. When it reaches the desired temperature (say 80oC) click on the Stop Heating button. When the temperature falls to 70oC, start the
stop watch. The time reading is taken for every 5o fall of temperature. The user can click on the 'Show Graph' checkbox to see a graph that
is initially blank. To plot the graph, click on the Plot Graph button. The graph is plotted by noting the temperature along the Y axis and time
along the X axis.

The graph is shown below. The next is the reset button. It resets the simulator to its default values.
Example :

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10/11/24, 2:08 PM Newton's Law of Cooling (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

The user can repeat the experiment to change the material, liquid and temperature TH.

The values entered in both variable menu and measurement menu are default values. The user can do the experiment using different options
by selecting the corresponding icons.

Measurement Menu:
In the measurement menu the user can view the measured temperature reading and the time for cooling.

Procedure for Real lab

The calorie meter is filled 2/3rd with the given liquid and is heated to a temperature of 80oC. This liquid will act as a hot body which is
subjected to cooling. The thermometer is inserted in to the calorimeter. When the temperature reading is 70oC the stopwatch is started. The
time readings are noted for every 5o fall of temperature up to the room temperature. The readings are tabulated. A graph is drawn with
temperature θ along Y axis and time (t) along X axis, dθ/dt is found by taking slopes to tangents drawn at various
temperatures on the cooling curve. Hence Newton's law of cooling is verified.
Observations and Calculations

Temperature
Time (s)
(0C)

Slope dθ/dt = .............................

Result
Newton's Law of Cooling is verified.

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10/11/24, 2:08 PM Newton's Law of Cooling (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapeetha…

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10/11/24, 2:04 PM Black Body Radiation: Determination of Stefan's Constant (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences…

Black Body Radiation: Determination of Stefan's Constant

Aim:
Determination of Stefan- Boltzmann constant σ .

Apparatus:
Heater, temperature-indicators, box containing metallic hemisphere with provision for water-
flow through its annulus, a suitable black body which can be connected at the bottom of this
metallic hemisphere.

Principle:
A black body is an ideal body which absorbs or emits all types of electromagnetic radiation. The term ‘black
body’ was first coined by the German physicist Kirchhoff during 1860’s. Black body radiation is
the type of electromagnetic radiation emitted by a black body at constant temperature. The spectrum of this radiation is specific and its
intensity depends only on the temperature of the black body. It was the study of this phenomenon which led to a new branch of physics
called Quantum mechanics.

According to Stefan’s Boltzmann law (formulated by the Austrian physicists, Stefan and Boltzmann), energy radiated
per unit area per unit time by a body is given by,

xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»=Ãâ

Where R = energy radiated per area per time, Є = emissivity of the material of the body, σ =
Stefan’s constant = 5.67x10-8 Wm-2K-4, and T is the temperature in Kelvin scale.

Josef Stefan Ludwig Boltzmann

For an ideal black body, emissivity Є=1, and equation (1) becomes,

xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»=Ãâ

The block diagram of experimental set up to study the blackbody radiation is given below.

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10/11/24, 2:04 PM Black Body Radiation: Determination of Stefan's Constant (Theory) : Heat & Thermodynamics Virtual Lab : Physical Sciences…
figure(1)

This setup uses a copper disc as an approximation to the black body disc which absorbs radiation from the metallic hemisphere as shown in
fig (1). Let Td and Th is the steady state temperatures of copper disc and metallic hemisphere respectively. Now according to the equation
(2), the net heat transfer to the copper disc per second is,

xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»Ã

Where A is the area of the copper disc and ΔQ= (Qh-Qd).

Now, we have another equation from thermodynamics for heat transfer as,

xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»Ã

Where ‘m’ mass of the disc, ‘Cp’’

specific heat of the copper, dT/dt is the change in temperature per unit time.

Equating equations (3) and (4),

xmlns=¨http://www.w3.org/1998/Math/MathML¨»«miȤ#963;«/mi»«miÃ

Hence,

xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo

Applications:
1. Determination of temperature of Sun from its energy flux density.
2. Temperature of stars other than Sun, and also their radius relative to the Sun, can be approximated by similar means.
3. We can find the temperature of Earth, by equating the energy received from the Sun and the energy transmitted by the Earth under black
body approximation.

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10/11/24, 2:11 PM The Study of Phase Change (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapee…

The Study of Phase Change

Cooling Curve:

The cooling curve has three distinct regions.

The cooling region PQ for the liquid
QR for the phase change
RS for the solid

The temperature corresponding to the horizontal region QR of the

cooling curve gives the transition temperature. The time for phase
change is noted from the graph. It is given by the interval for the
horizontal region QR of the graph. The rate of cooling r = dθ/dt
in the region RS is also calculated.

Procedure for doing the Simulator:

From the combo box Select Substance select the desired sample.

The mass of the substance can be varied by using the slider Mass of
the substance.

The temperature of the surrounding can be selected by using the slider Surrounding Temperature.

The mass, radius and thickness of the boiling tube can be varied by using the sliders given under the heading Boiling tube.

The experiment can be started by clicking on the Start the Experiment button.

Then the sample in the boiling tube begins to melt.

The temperature of the sample can be noted from the digital thermometer given in the simulator.

Also time can be noted from the stop-watch given in the simulator.

The time-temperature observation is also plotted there.

There is an option Show Result. By clicking it, we can obtain the melting point and the transition time of the sample.

Procedure for doing Real Lab:

The mass m1 of the empty boiling tube is taken.

Sample of mass m2 is put into the boiling tube. It is melted by keeping the test tube immersed in hot oil bath. The sample melts into clear
liquid.

When it is melted completely, the test tube is taken out, wiped dry, suspend in air and allowed to cool.

A thermometer is immersed into the melt. A stop-watch is started and the temperature is noted for every equal interval of time. The time-
temperature observation is taken till the liquid get frozen into solid and gets cooled to room temperature.

Draw a cooling curve by taking time along the X- axis and temperature along Y-axis. The temperature corresponding to the horizontal
region will give the transition temperature.

The time for the transition time is also noted from the graph. The experiment is repeated for different samples.

Observations and Calculations:

Mass of the sample, m2 =

………………kg
Specific heat capacity of glass,C1 =

………………Jkg-1K-1
Specific heat capacity of sample,C2 =

………………Jkg-1K-1

Time in Temperature in
minutes oC

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10/11/24, 2:11 PM The Study of Phase Change (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidyapee…

Result:
The cooling curve for the phase change of the sample is studied.

Transition time of the sample = …………. min

Melting point of the sample = ........................oC

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10/11/24, 2:12 PM Thermo Couple-Seebeck Effect (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Sciences : Amrita Vishwa Vidya…

Thermo Couple-Seebeck Effect

Performing the simulation

1. The user has to select the type of thermocouple from the 'Choose ThermoCouple Type' combo box.
2. Adjust the temperature slider to a specific temperature.
3. The emf generated can be viewed through the voltmeter.
4. The temperature versus emf graph can be analyzed.

Variable Region:

1. Choose ThermoCouple Type: The user can select different kinds of thermocouple with this combo box.
2. Hot Temperature Slider: This slider is used to change the temperature of the hot junction.
3. Reference Temperature Slider: This slider is used to change the reference temperature.

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10/11/24, 2:04 PM Black Body Radiation: Determination of Stefan's Constant (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Scien…

Black Body Radiation: Determination of Stefan's Constant

Procedure for performing real lab:

1. Remove the disc from the bottom of the hemisphere and switch on the heater and allow the water to flow through it.
2. Allow the hemisphere to reach the steady state and note down the
temperature T1, T2, T3 .
3. Fit the disc (black body) at the bottom of the hemisphere and note down
its rise in temperature with respect to time till steady state is reached.
4. A graph is plotted with temperature of disc along Y-axis and time along X-
axis as shown.
5. Find out the slope dT/dt from the graph.

Procedure for performing simulator:

1. Choose desirable values of water temperature, surrounding temperature, mass and radius of the disc using the sliders.
2. Click the "Power ON" button and wait till T1, T2 ,T3 reach steady state. Note down its values.
3. Putting T4 button, click "Fit the disc'' option.
4. Note down T4 at different intervals of time till it reaches steady state.

5. Plot Temperature-Time graph and determine its slope .

6. Determine Stefan's constant '

«math
xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«/

' using the given formula.

Observations:

Calculations:
Mass of the copper disc = ...... kg

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10/11/24, 2:04 PM Black Body Radiation: Determination of Stefan's Constant (Procedure) : Heat & Thermodynamics Virtual Lab : Physical Scien…
Specific heat of copper = ...... Jkg-1
Radius of the disc = ..... m
Area of the disc = ......m2

Slope of the graph = ……Ks-1

Substituting the values in the given expression,

«math
xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo

=
……………………ââ‚Â
Wm-2K-4

Result:
Stefan-Boltzmann’s constant Ïà † ’
=……………. Wm-2K-4

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