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HEAT-1
THERMOMETRY
This is the science of temperature and its measurement.
TEMPERATURE
The temperature of a body is a number which expresses its degree of hotness or coldness on some chosen scale.
It is measure of how hot or cold the body is.
THERMOMETERS
A thermometer is an instrument designed to measure the temperature of a body.
Thermometers use some measurable property of a substance (thermometric property) which is sensitive to temperature.
Thermometric property
Is that property in which quantity value of a thermometer varies linearly and continuously with temperature
The thermometric property is also called physical property of a thermometer.
Examples of thermometric properties (physical properties) of a thermometer are:
- Length of liquid column in a glass tube
- Volume of a gas at constant pressure
- Pressure of a gas at constant volume
- Electrical resistance of a platinum wire
- Electromotive force of a thermo-couple
QUALITIES OF A THERMOMETRIC PROPERTY
A thermometric property must have:
- A marked degree of expansion for a small temperature rise
- A uniform expansion rate
- Good thermo conductivity
- High boiling point and low freezing point (if it is liquid)
TEMPERATURE SCALES
- CELSIUS SCALE
This is a temperature scale in which the fixed points are the temperatures at standard pressure of ice in equilibrium with water (0
) and water in equilibrium with steam (100
)
The scale between these two temperatures is divided into 100 equal parts and each part is called a degree.
The temperature on this scale is expressed in degree Celsius (
)
- FAHRENHEIT SCALE
This is a temperature Scale in which the temperature of boiling water is taken as 212
and the temperature of pure melting ice is taken as 32![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDE0IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
The interval between these two reference temperatures is divided into 180 equal parts and each part is called degree Fahrenheit (
)
To convert this scale into degree centigrade (
), the formula is:
- THERMODYNAMIC TEMPERATURE SCALE
This is the standard temperature scale adopted for scientific measurement.
Thermodynamic temperature is denoted by the symbol T and is expressed in Kelvin, K.
The lowest possible temperature which can be measured by this scale is assigned the value zero (OK) called absolute zero
It is the lowest temperature theoretically attainable at which the random motion of molecules and atoms in a substance is at minimum.
The temperature of a substance cannot be lowered further by decreasing the random motion.
Thermodynamic temperature is also called absolute temperature. The degree centigrade is equal in magnitude to temperature in Kelvin i.e a change of temperature in
is equal to a change of temperature in Kelvin.
NECESSARY CONDITIONS FOR THE TEMPERATURE SCALE TO BE ESTABLISHED
In order to establish a temperature scale one requires;
(1) SOME PHYSICAL PROPERTY OF A MATERIAL
The physical property of a material should vary linearly and continuously with temperature.
Examples
- The length of liquid column in a glass tube varies linearly and continuously with temperature.
Length temperature ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDg3IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
= k + 0 ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDg3IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Compare y = + ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDY4IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
This is a linear relationship
- The volume of a gas at constant
pressure varies linearly and continuously with temperature.
Volume temperature ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5MyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDkzIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
- V = K T + 0
Compare y = + ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDczIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
This is a linear relationship
- The pressure of a gas at constant volume varies linearly and continuously with temperature
- P = K T + 0
Compare y = + ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDczIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
This is a linear relationship
(2) FIXED POINTS
A fixed point is a temperature that can be accurately reproduced to enable it to be used as a basis of a temperature scale.
It is a single temperature at which it can confidently be expected that a particular physical event ( e.g the melting of ice under specific conditions) always takes place.
The three fixed points are:
- Ice point
Is the temperature at which pure ice can exist in equilibrium with water pure at standard atmospheric pressure (i.e. at 760mmHg).
- Steam Point
Is the temperature at which pure water can exist in equilibrium with its vapor at standard atmospheric pressure.
- Triple point
Is that unique temperature at which vapor, liquid and solid phases of a substance exist in equilibrium.
The triple point is particularly useful, since there is only one pressure at which all three phases (solid, Liquid and gas) can be in equilibrium with each other.
Example, For water the triple point is 273.16K and it occurs at a pressure of 611.2Pa
DISAGREEMENT BETWEEN SCALES
Different materials do not expand in quite the same way over a wide range of temperatures.
Thermometric properties do not keep in step as the temperature changes.
Consequently, if we calibrate different kinds of thermometers by using ice point and steam point as the reference marks they will not agree precisely (accurately).
Different results are obtained when different kinds of thermometers are used to measure the same temperature except at the calibrated fixed point.
THE TEMPERATURE SCALE EQUATION
When there is a change of temperature, the physical property of a material also changes.
Since the physical property of a material varies linearly and continuously with temperature then we have:
Let X be physical property of a material
Let X0 be physical property of a material at ice point (0
)
Temperature | Physical Property |
0 | X0 |
100 | X100 |
CASE 1
When the temperature changes from 0
to 100![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDE0IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Change in temperature = 100 – 0 ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDU0IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
= 100![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDE0IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Change in property =
–
But change in temperature
change in thermometric property
100
( – )
100 = K( – ) …………………………….(1) ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNzgiIGhlaWdodD0iMjMiIHZpZXdCb3g9IjAgMCAxNzggMjMiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+)
Where K = constant of proportionality
CASE 2
When the temperature changes from 0![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NiIgaGVpZ2h0PSIyNyIgdmlld0JveD0iMCAwIDY2IDI3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Change in temperature = ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4MiIgaGVpZ2h0PSIyNSIgdmlld0JveD0iMCAwIDgyIDI1Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
= ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMCIgaGVpZ2h0PSIxOSIgdmlld0JveD0iMCAwIDEwIDE5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Change of the thermometric property =
–
But change in temperature
change in thermometric property
Where k = constant of proportionality
Dividing ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1MSIgaGVpZ2h0PSIzNSIgdmlld0JveD0iMCAwIDUxIDM1Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
RELATIONSHIP BETWEEN PHYSICAL PROPERTY OF A MATERIAL AND TRIPLE POINT
Consider a physical property P of a material which varies linearly and continuously with temperature.
Let P Trip be physical property of a material at triple point temperature T Trip
Since change in temperature
change in thermometric property we have
T Trip
P Trip
Where K = constant of proportionality
Let PT be physical property of a material at a temperature T (in Kelvin)
Similarly T
PT
Dividing ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1MSIgaGVpZ2h0PSIzNSIgdmlld0JveD0iMCAwIDUxIDM1Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Equation (3) above can also be written as:
T =
x T Trip
– For water T Trip = 273.16K
TYPES OF THERMOMETERS
There are so many types of thermometers but they all have common fact that they depend on some physical property of a material which changes with temperature.
Some important thermometers are: – (i) Liquid in glass thermometers
- Gas thermometers
- Platinum resistance thermometers
- Thermocouple thermometers
- Radiation thermometers (Pyrometers)
(i)LIQUID IN GLASS THERMOMETERS
One of the most familiar thermometer uses mercury as a thermometric liquid
In this type of thermometer the length of mercury in a glass tube is the thermometric property of a material when the temperature changes.
This means that in the temperature scale equation,
becomes length ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDEwIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
The temperature
of the thermometer in terms of length
of mercury is given by:
When,
= length of mercury at ice point
ADVANTAGES OF USING MERCURY IN THE LIQUID GLASS THERMOMETER
The use of mercury has the following advantages.
- Its boiling point 357
and its freezing point is – 36
Therefore it can be used over a wide range of temperature.
- Its expansion is nearly uniform over the ordinary range of temperatures.
This makes the calibration of the thermometer easier.
- It can be easily seen through glass because it is opaque and shining liquid.
- It does not wet glass
no mercury remains on the sides of the glass tube when the mercury level falls.
- It has low specific heat capacity. Therefore it does not absorb much heat from the body whose temperature is to be measured.
DISADVANTAGE OF USING MERCURY IN THE LIQUID IN GLASS THERMOMETERS
It cannot be used to measure very low as well as very high temperatures.
(ii) GAS THERMOMETERS
In most accurate work, temperatures are measured by gas thermometers.
There are two types of gas thermometers:
- Constant volume gas thermometer
- Constant pressure gas thermometer
JOLLY’S CONSTANT VOLUME GAS / AIR THERMOMETER
B1 is a glass bulb containing dry air
B2 is a glass tube containing mercury
B1 is connected to B2 by means of a capillary tube E bent twice at right angles
B3 is a glass tube containing mercury which is open the atmosphere at its upper end.
There is a fixed mark ―O‖ on the glass tube B2
The volume of air in B1 is maintained constant by raising or lowering the glass tube B3 until the mercury in B2 is at the fixed mark ―O‖.
OPERATION
When the thermometer is in use the bulb
is placed inside the enclosure whose temperature is required.
Keeping the volume of air in B1 constant by raising or lowering the glass tube B3, the pressure of air in B1 at ice point (0
), steam point (100
) and at the unknown temperature
) are determined.
If P denote pressure of a gas/air at constant volume, then one can talk of pressure at 0
,
100 and as P0, P100 and
respectively ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OSIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDY5IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Now, the unknown temperature
is given by:
Gas thermometer is an ideal thermometer because the increase in volume or pressure of a gas with temperature is independent of the nature of the gas.
ADVANTAGES OF USING GAS THERMOMETER
The gas thermometer has the following advantages:
- It is more sensitive than liquid in glass thermometer because the expansion of gases is many times greater than that of any liquid.
- The expansion of the gas is uniform and regular.
- Gas scale temperatures degree with absolute scale of temperature.
- It can be used to measure very low as well as very high temperatures.
Example
– Hydrogen gas thermometer can measure temperature from – 200
to 500![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDE0IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
DISADVANTAGES OF USING GAS THERMOMETERS
The gas thermometer has the following disadvantages: –
- Its use is inconvenient due to its very large size.
- The air in the capillary tube is not at the temperature being measured.
- It cannot be used to measure the temperature of a liquid available in small quantity.
- It is not a direct reading thermometer. ie require skill
SOURCES OF ERRORS WHEN USING GAS THERMOMETERS
- The bulb expands
- Air is not an ideal gas
(iii)The air in the capillary tube is not at the temperature being measured
PLATINUM RESISTANCE THERMOMETER
The Platinum resistance thermometer is based on the principle that the electrical resistance of a pure metal increases with increasing in temperature and vice versa.
Experiments show that the resistance of a pure metal at any temperature
is given by:
Where R0 = Resistance at 0 , = Resistance at a temperature
It can be shown that where ‘a’ and ‘b’ are physical constant ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyMzciIGhlaWdodD0iNTIiIHZpZXdCb3g9IjAgMCAyMzcgNTIiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+)
In practice”b” is much less than ―a‖ and hence we can ignore the term b
2
Here ―a‖ is called temperature coefficient of resistance of the material of the wire (symbol,
For platinum wire
= 3.8 x 10-4/
-1
CONSTRUCTION
A sample from a platinum resistance thermometer consist of a platinum wire that would be around the mica former.
The wire is enclosed in a protective tube of quartz, glass or porcelain tube depending upon the type of application and temperature range.
The platinum wire is used because of its high temperature coefficient of resistance and high melting point (1773
)
Therefore, considerable change in resistance occurs for a relatively small change in temperature.
OPERATION
The platinum resistance thermometer forms one of the four arms of the Wheatstone bridge.
R1 and R2 are fixed resistors while R3 is a variable resistor.
The bridge is often kept at a considerable distance from the testing point
Under ordinary condition the bridge is balanced, that means the galvanometer shows no reading.
When the temperature changes the resistance r of the resistance thermometer also change
Consequently, the bridge no longer remains balance and some current flows through the galvanometer.
The change in resistance (and hence current through G) is a measure of the magnitude of temperature.
The accuracy of the platinum resistance thermometer depends on how accurately the bridge can be balanced.
Let R0, R100 and
be resistance of platinum wire at ice point (0
), steam point (100
) and at the unknown temperature
respectively
The temperature
of the scale is given by:
ADVANTAGES OF USING PLATINUM RESISTANCE THERMOMETER
- High sensitivity (0.00005
)
- Small size
- Measurements can be made over a wide range (260
– 1200
)
DISADVANTAGES OF USING PLATINUM RESISTANCE THERMOMETER
- High cost
- Requires additional equipments such as the bridge circuit, power supply etc.
- Larger size than thermocouple
(iv)THERMOCOUPLE THERMOMETER
A thermocouple is a device consisting of two dissimilar metal wires welded together at their ends.
A thermoelectric (
) is generated in the device when the ends are kept at two different temperatures.
The magnitude of the
generated is related to the temperature difference between the two junctions.
This enables a thermocouple to be used as a thermometer over a limited temperature range
OPERATION
One of the two junctions called the hot or measuring junction is placed at the temperature to be measured.
The other junction( the cold or reference junction) is maintained at a known reference temperature (usually 0![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNCIgaGVpZ2h0PSI1MiIgdmlld0JveD0iMCAwIDI0IDUyIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
The
generated is measured by a suitable millvoltmeter or a potentiometer incorporated in the circuit.
The amount of the
generated depends upon the temperature difference between the hot and the cold junction
The greater the
the greater is the temperature difference between the junctions.
VARIATION OF THERMOELECTRIC
WITH TEMPERATURE
When the cold junction of a given thermocouple is kept constant at 0
and the hot is varied. The e. m. f is found to relate with the temperature ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMjQiIGhlaWdodD0iMTU0IiB2aWV3Qm94PSIwIDAgMzI0IDE1NCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgc3R5bGU9ImZpbGw6I2NmZDRkYjtmaWxsLW9wYWNpdHk6IDAuMTsiLz48L3N2Zz4=)
difference junction by the equation
Where A
B are constants.
This is a parabolic equation and hence a graph of E against
is a parabola of the nature shown in the figure below.
Where
Temperature of the cold junction
Neutral temperature (
)
Is the temperature at which the
of a thermocouple is maximum.
When the temperature is increased beyond the thermoelectric e. m. f decreases untill it becomes zero when the temperature is called inversion temperature. ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NiIgaGVpZ2h0PSI0OSIgdmlld0JveD0iMCAwIDU2IDQ5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Inversion Temperature
Is the temperature to which the hot junction of a thermocouple must be raised in order that the thermoelectric e. m. f in the whole circuit becomes zero.
From the graph above
2 = + ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMDUiIGhlaWdodD0iMjMiIHZpZXdCb3g9IjAgMCAxMDUgMjMiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+)
From the relationship between E and ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDEwIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
E ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDg3IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Differentiating this equation with respect to ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDEwIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
When
= 0 (slope of tangent at neutral temp)
0 = A + 2B
n
2B![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1OSIgaGVpZ2h0PSIyOCIgdmlld0JveD0iMCAwIDU5IDI4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
EXPRESSION OF INVERSION TEMPERATURE
From the relationship between E and ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDEwIDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
E = A – B 2 ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0OSIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDQ5IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
When E = 0 then = ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0NiIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDQ2IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
- When the inversion temperature is exceeded the thermoelectric (e. m. f) in the thermocouple is reversed.
- The use of a thermocouple is restricted in the temperature range between 0 and neutral temperature
It is because, beyond neutral temperature
the thermoelectric e. m. f decreases with increasing temperature
ADVANTAGES OF USING THERMOCOUPLES
- They have small heat capacities.
Therefore they have very little effect on the temperature of the body they are measuring.
- They can measure rapidly fluctuating (changing) temperatures.
- They are more accurate.
- They are cheap and easy to use
- They have a wide range of temperature measurement (-200
to 1500
) depending upon the metals used.
DISADVANTAGES OF USING THERMOCOUPLES
- Reference temperature has to be kept constant.
- As the output voltage is less than 10mV a very sensitive meter is required. (iii) The variation of e.m.f with temperature is non-linear
(v) RADIATION THERMOMETERS (PYROMETERS)
For measuring very high temperatures radiation thermometers (Pyrometers) are used.
In these instruments high temperatures are measured by observing the radiation from the hot body.
The thermal radiation from the hot body is compared in terms of color with thermal radiation from the lamp filament.
When a pyrometer is used a hot wire filament in the pyrometer is viewed against a glowing object.
The filament current increased from zero until it makes the filament exactly the same color as the following object.
A meter in series with the filament can then be calibrated directly in terms of source temperatures, known using the laws of radiation.
They fall into two classes:
- Total radiation py
rometer
Which respond to the total radiation from the hot body
- Optical pyrometer
Which respond only to the visible light
Problem 01
A thermometer uses mercury as liquid in glass experiments show that the length of mercury at 0
and 100
are 5cm and 7cm respectively. At a certain temperature the length of the mercury is found to be 6.5cm, find this certain temperature. (Answer = 75 ) ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDU3IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Problem 02
The pressure recorded by a constant volume gas thermometer at a Kelvin temperature T is 4.80 x 104Nm-2.
Calculate T if the pressure at triple point 273.16K is 4.20 x 104Nm-2. (Answer. T = 312K) Problem 03
The resistance of a platinum wire at a temperature
, measured on gas scale is given by
= R0 (1 + a + b 2) ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0NSIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDQ1IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Where
3.8 x 10-3 and
–5.6 x 10-7
What temperature will the platinum thermometer indicate when the temperature on a gas scale is 200![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNCIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDE0IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Problem 04
The pressure of air in a constant volume gas thermometer is 80cm and 109.3cm at 0
and
100
respectively. When the bulb is placed in hot water, the pressure is 100cm. calculate the temperature of hot water
Problem 05
The resistance of a platinum resistance thermometer is 100
at room temperature of 25
. In an experiment for measurement of temperature, the resistance of the thermometer is found to be 115.68
. find the value of temperature given that the temperature coefficient of resistance of platinum is 0.004/
.
Problem 06
A constant mass of a gas maintained at constant pressure has a volume of 200
at the temperature of melting ice, 273.2
at the temperature of water boiling under standard pressure and 525.1 at the normal boiling point of sulphur. A platinum wire has resistances of 2.00 , 2.778 , and 5.280
at these temperatures. Calculate the values of boiling- point of sulphur given by the two sets of observations and comment on the results. ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MSIgaGVpZ2h0PSI0OSIgdmlld0JveD0iMCAwIDcxIDQ5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Problem 07
In the thermocouple, the temperature of the cold junction is 10
while the neutral temperature is 270
. What is the value of temperature of inversion?.
Problem 08
In a certain thermocouple the thermo e. m. f E is given by
E =
+
Where
is the temperature of the hot junction and the cold junction being at 0
.
If = 10 V / and
= , find ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5NiIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDk2IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
- The neutral temperature
- The temperature of inversion
Problem 09
- What does one require in order to establish a scale of temperature?
- A Copper – constant thermocouple with its cold junction at 0
had an EMF of 4.28mV with its other junction at 100 . The EMF becomes 9.29mV when the temperature of the hot junction was 200 . If the EMF E is related to the temperature different
by the equation E = A + B 2, Calculate
- The values of A and B
- The range of temperature of which E may be assumed proportional to
without incurring an error of more that 1%?
Problem 10
The resistance
of a platinum varies with temperature t according to the equation
R0 (1 + 8000bt – bt2) where “b” is a constant.
Calculate the temperature on platinum scale corresponding to 400
on the gas scale
Problem 11
- Define the thermodynamic temperature scale
- The resistance of a platinum resistance thermometer is 1.20
when measuring a Kelvin temperature T of a body and 1.00
at the triple point of water. Find T and its centigrade equivalent.
Problem 12
- What do you understand by the terms
- Thermodynamic temperature scale
- Triple point of water
- The resistance of a platinum wire at temperature T
measured on a gas scale is given by
R (T) = R0 (
)
What temperature will the platinum thermometer indicate when the temperature on the gas scale is 200
?
(Take
3.8 x 10-3 and
5.6 x 10-7)
Problem 13
- Define
- Thermodynamic temperature scale
- How thermodynamic temperature donated and what is its SI unit?
- Explain why a gas thermometer is seldom used for temperature measurement in the laboratory?
- Study the table below and answer the questions which follow:
- Calculate the temperature of the room for each thermometer
- Explain why thermometers disagree in their values of room temperature.
- What are the advantages of gas thermometer over liquid in-glass thermometers?
Problem 14
(a) (i) Describe how mercury in glass thermometer could be made sensitive.
(ii) A sensitive thermometer can be used to investigate the difference in temperature between the top and bottom of the waterfall. Calculate the temperature difference of the water fall 50m high.
(b) (i) Platinum resistance thermometer and constant volume gas thermometer are based on different thermometric properties but they are calibrated using the same fixed points. To what extent are the thermometers likely to agree when used to measure temperature near the ice point and near the steam point.
(ii)The resistance of the element of a platinum resistance thermometer is 2.0
at ice point and 2.73
at steam point. What temperature on the platinum resistance scale would correspond to resistance value of 8.34 and when measured on the gas scale the same temperature will correspond to a value of 1020 ? Explain the discrepancy. ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1MyIgaGVpZ2h0PSI0OSIgdmlld0JveD0iMCAwIDUzIDQ5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Problem 15
(a). (i) What is meant by a thermometric property of a substance?
(ii) What qualities make a particular property suitable for use in practical thermometers
(b) Explain
- Why at least two (2) fixed points are required to define a temperature scale?
- Mention the type of thermometer which is most suitable for calibration of thermometers.
This is the transfer of heat energy from one body or system to another as a result of difference in temperature. In general heat energy transfers from the region of higher temperature to the region of lower temperature.
WAYS OF HEAT TRANSFER
There are three ways by which heat can be transferred
- Conduction
- Convection
- Radiation
THERMAL CONDUCTION This is the process in which heat flows from the hot end to the cold end of the solid body without there being any net movement of the particles of the solid.
MECHANISM OF THERMAL CONDUCTION
MECHANISM 1
The molecules of a solid vibrate about their fixed positions with an energy that increases with temperature.
When a part of the solid is heated, the molecules there start vibrating more violently.
Since neighboring molecules are bound to each other, a molecule vibrating with larger energy will transfer some of its energy to its neighbors which in turn will transfer energy to the next neighbors and so on.
MECHANISM 2
In case of metals heat energy can also be transported by the free electrons.
Since the electrons are very small, they can travel rapidly around throughout the specimen transferring energy by collision to other electrons and other molecules.
Hence, the electrons are more effective in transferring energy from the hotter part to the colder part of the material than the mechanism explained above (mechanism 1)
This explains why thermal conduction in metals is much more than that in insulators
In metals heat energy is mainly carried by the free electrons although some energy is carried by intermolecular vibration.
IMPORTANT TERMS
- RATE OF HEAT FLOW
Symbol, ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5MiIgaGVpZ2h0PSI0OSIgdmlld0JveD0iMCAwIDkyIDQ5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
This is the heat flow per unit time in a material
- TEMPERATURE DIFFERENCE
Symbol ( – ) or d ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5NSIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDk1IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
This is the difference between higher and lower temperatures.
Heat flows from the region of higher temperature to the region of lower temperature and if
> then,
Temperature difference =
–
- TEMPERATURE GRADIENT
Symbol
or
This is the temperature difference per unit length of the material.
It is a fall of temperature with distance between the ends of the body in the direction of heat flow.
Temperature gradient =
=
- STEADY CONDITION
This is an equilibrium point in a material when at every point the temperatures are constant.
- LAGGED MATERIAL
A material enclosed by an insulator (bad conductor of heat) so that the heat loss to the surrounding is negligible.
- UNLAGGED MATERIAL
A material which is not enclosed by an insulator so that the heat is lost to the surrounding.
TEMPERATURE DISTRIBUTION ALONG THE CONDUCTOR
1. UNLAGGED CONDUCTOR
Consider an unlagged metal bar AB whose ends have been soldered into the metal tanks H and C
H contains boiling water and C contains ice water.
Heat flows from the hot end to the cold end of the bar and when the conditions are steady the temperature
are measured at points along the length of the bar.
This happens simply because some amount of heat is lost to the surrounding by convection and radiation.
2. LAGGED CONDUCTOR
If the metal bar is well-lagged with a bad conductor of heat such as asbestos and wool the temperature now falls uniformly from the hot end to the cold end of the bar.
A graph of temperature against length of the bar is shown below:
Since the metal bar is well-lagged no heat is lost to the surrounding and a graph of fall of temperature against length of the bar is a straight line (see figure above)
THERMAL CONDUCTIVITY
It is measure of the ability of a material to conduct heat.
Consider a conductor of length L of cross – sectional area A
Let and be temperature on the opposite sides of the conductor with
> ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NyIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDY3IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
Experiments show that the heat flow per second
from the hot sides to the cold side of the conductor is:
- Directly proportional to the cross-sectional area A of the conductor
- Directly proportional to the temperature difference
– ) between the two sides
- Inversely proportional to the perpendicular distance between the concerned faces
Combining the above three factors:
Where K = constant of proportionality called coefficient of thermal conductivity (thermal conductivity) of the material.
Equation (1) above assumes that:
- The opposite sides are parallel
- There is no heat loss through the sides.
From equation (1)
Definition
The coefficient of thermal conductivity K of a material is the rate of flow of heat per unit area per unit temperature gradient when the heat flow is perpendicular to the faces of a thin parallel – sided slab of the material under steady state conditions.
UNIT OF K
From equation (2)
K = ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OCIgaGVpZ2h0PSI1NCIgdmlld0JveD0iMCAwIDY4IDU0Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
= ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMTMiIGhlaWdodD0iNTIiIHZpZXdCb3g9IjAgMCAxMTMgNTIiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+)
= ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMTMiIGhlaWdodD0iNDAiIHZpZXdCb3g9IjAgMCAxMTMgNDAiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+)
Hence, the SI unit used Wm -1K-1 Equation (1) can be written as:
Where
= Temperature gradient
The
sign show that the heat flows in the direction of decreasing temperature i.e the temperature
diminishes as the length
increases. The value of K for some common substances at room temperature are as shown in the table below:
Substance | K in Wm -1K-1 |
Silver | 418 |
Copper | 385 |
Aluminum | 238 |
Iron | 80 |
Lead | 38 |
Mercury | 8 |
Glass (Pyrex) | 1.1 |
Brick | -1 |
Rubber | 0.2 |
Air | 0.03 |
Substance for which
is small is bad conductors of heat.
Substance for which k is large conducts heat rapidly and are said to be good conductors of heat.
COMPOSITE BARS
A composite bars is that bar consisting of two or more metal bars of different materials joined end to end.
Consider a composite bar made of different materials of coefficient of thermal conductivities K1 and K2 respectively
Let A be cross sectional area of the bar
Assuming the bar is well – lagged so that no heat leaves from it.
Condition
At steady state condition, the heat flowing into one end of the bar is equal to that flowing out of the other end.
Where , and are the temperatures at the ends of the bars respectively. ![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NiIgaGVpZ2h0PSIyMyIgdmlld0JveD0iMCAwIDg2IDIzIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==)
THERMAL RESISTANCE (R)
From the heat conduction equation:
This equation can be linked to Ohm‘s law for electricity
I =
From equation (1) and equation (2) above both
and I are flow quantities.
In equation (1) the heat flows per second
produced by a temperature difference
.
In equation (2) the flow of current I ( = charge flow per sec) is produces by potential difference V
Thus, the quantity
is thermal Equivalent of
Where
= conductor length
K = Thermal conductivity
A = across- sectional area of the conductor.
Alternative expression of R From the heat conduction equation:
But
=