HEAT AND TEMPERATURE

Heat and Temperature:
Heat is a form of Energy that is transferred from one point to another due to change in temperature. It is a form of energy that flow from a point of higher temperature to a point of lower temperature. It can also be defined as a measure of the total internal energy of a body. Heat is a vector quantity. It is measured in Joule.

While

Temperature is the degree of hotness or coldness of a body. It is a measure of the average kinetic energy of the molecules that make up the body. It is a s lar quantity. It is measured in degree Celsius (°C) or kelvin (K).

Measurement Of Temperature:
The instrument that is used to measure temperature is called thermometer. The thermometers used any physical property of  substance which varies with temperature and is easily measurable as means measuring temperature.
Thermometric Substances:
Thermometric s are substances whose physical properties are used in the construction of thermometers.

Types Of Thermometers,  Thermometric Substances and physical properties.

Type of thermometer:  

1. Liquid in glass   

    thermometric substance:  Mercury or Alcohol.      

    Physical property:  Change in volume of liquid with temperature.

2. Gas thermometer

    thermometric substance:  Gas.

    Physical property:  Gas pressure changes with temperature.

3. Resistance thermometer

    Thermometric Substance:  Resistance wire

    Physical Property:  Electrical resistance change with temperature.

4. Thermocouple

    Thermometric Substance:  Two dissimilar wires

    Physical Property:  Change in electric potential difference between two metal                                                  junctions at different temperatures.

5. Bimetallic thermometer

    Thermometric Substance:  Two dissimilar metals

  Physical Property:  Different expansion off the metametals.the bimetallic strip.

Temperature Scale Of Thermometer:

A thermometer has two reference temperatures or fixed points. They are the Upper Fixed Point and the Lower Fixed Point.

The Upper Fixed Point:

Upper fixed point is the temperature of steam from pure water boiling at standard atmospheric pressure of 760 mm of mercury ( 760mmHg).

The Lower Fixed Point:

The lower fixed point is the temperature of pure melting ice  block at standard atmospheric pressure of 760mm of mercury, ( 760mmHg ).

Fundamental Interval:

Fundamental interval is the difference between the upper fixed point and the lower fixed point of a thermometer. The calibration of the fundamental interval of a thermometer depends on the temperature scale chosen.

Formula For Calculating Fundamental Interval:

Fundamental Interval = upper fixed point – lower fixed point.

Therefore,

Fundamental interval of degree Celsius = 100° - 0° = 100°C

Fundamental interval of Kelvin scale = 212 – 32 = 180K

Fundamental interval of Fahrenheit scale = 373 – 273 = 100°F

Types Of Temperature Scales:

In temperature measurement, three types of scales are currently used in measuring temperature. They are:

I. The Celsius scale

II. The Fahrenheit scale

III. The Absolute or thermodynamic or kelvin scale

Diagram Of Temperature Scale: 

The figure shows the three different temperature scales, in °C, °F and K, that are used in measuring temperature.

Conversion Of Temperature From One Scale To Another:
Conversion of temperature from degree Celsius (°C) to degree Fahrenheit ( °F ):
From the figure above, I will show and explain how to convert temperature from degree Celsius to degree Fahrenheit as follow:

                    AB/AC = DE/DF
(X – 0)/(100 – 0) = (Y – 32)/(212 – 32)
X/100 = (Y – 32)/180
(X/100)*180 = Y – 32
1.8*X = Y – 32

Note:
Where X is Temperature in degree Celsius while Y is temperature in degree Fahrenheit.
AB mean distance from A to B. AC means distance from A to C. DE means distance from D to E. DF means distance from D to F, and so on.
Worked Examples:
1. Change 25°C to temperature in Fahrenheit.

Solution:
Data given in the question:
Temperature in °C (X) = 25°C. Y = ?
Formula:              1.8*X = Y – 32
Substitution:       1.8*25 = Y – 32
Make Y the subject:    1.8*25+32 = Y. ➡ Y = 45 + 32.  ➡ Y = 77°F

2. Convert 120°F to degree Celsius.

Solution:
Data given in the question:
Temperature in °F, Y = 120°F
Formula:            1.8*X = Y – 32
Substitution:     1.8*X = 120 – 32.  ➡ 1.8*X = 88
Make X the subject:      X = 88 ÷ 1.8. ➡ X = 48.89°C

Note: you can equally solve the problems using the concept I used to obtain the formula. This can be done by simply substituting for X and Y respectively in the process and then follow the procedures to derive at the answers.

Conversion of temperature from degree Celsius (°C) to Kelvin (K):
Also, from the figure above, I will explain how to convert temperature from degree Celsius to temperature in Kelvin. This is illustrated in formula 2.

Note: X is temperature in degree Celsius while Z is temperature in Kelvin.
AB/AC = GH/GI ➡ (X – 0)/(100 – 0) = (Z – 273)/(373 – 273)
.                                  X/100 = (Z – 273) / 100
100 cancels 100:       X = Z – 273 or Z = X + 273
Where X is temperature in degree Celsius (°C) while Z is temperature in Kelvin (K)
Worked examples:
1. Calculate the value of 200°C in Kelvin.

Solution:
Data given in the question:
Temperature in °C, X = 200°C.
Formula:        X = Z - 273
Substitution:    200 = Z – 273
Make Z the subject: 200 + 273 = Z ➡ Z = 473 Kelvin

2. Given that the temperature of a body is 527kelvin, determine this value in degree Celsius.

Solution:
Data given in the quest:
Temperature in Kelvin, Z = 527K.
Formula:     X = Z – 273
Substitution:   X = 527 – 273. ➡ X = 254°C
Or
You can equally solve the problems using the concept I used to obtained the formula. You do this by substituting for X and Z respectively in the procedures and the follow the procedures to derive at he answers.

Thus:
From the question, Z = 527K.
Substitute for Z in the procedures
           B/AC = GH/GI ➡ (X – 0)/(100 – 0) = (Z – 273)/(373 – 273)
.                                  X/100 = (Z – 273) / 100
                                   (X - 0)/(100 – 0) = (527 -273)/(373 – 273)
                                   X/100 = ( 527 – 273 ) / 100
                                   X = 527 – 273 = 254°C

Conversion of temperature from degree Fahrenheit (°F) to Kelvin (K):
Also, from the figure far above, I will explain how to convert temperature from degree Fahrenheit to temperature in Kelvin. This is illustrated in formula 3.
From the figure,
                      DE/DF = GH/HI
                 (Y – 32)/(212 – 32) = (Z – 273)/(373 – 273)
.                (Y – 32)/180 = (Z – 273)/100
.                Y – 32 = 180*(Z – 273)/100
.                Y – 32 = 1.8*(Z – 273)

Worked Examples:
1. It was recorded that the temperature of a body was 320°F. Determine the value of this temperature in Kelvin.

Solution:
Data given in question:
Temperature in Fahrenheit, Y = 320°F
Formula:     DE/DF = GH/GI
                     (Y – 32)/(212 – 32) = (Z – 273)/(373 – 273)
Substitution:
                     (320 – 32)/180 = (Z – 273)/100
.                     288/180 = (Z – 273)/100
Make Z the subject:  288÷180*100 = Z – 273
                                     28800 ÷ 180 = Z – 273
.                                    160 = Z – 273
                                     160 + 273 = Z. ➡ Z = 433K
Or
Use direct substitution as follow:
Temperature in degree Fahrenheit Y = 320°F
Formula:      Y – 32 = 1.8*(Z – 273)
Substitution:    320 – 32 = 1.8*(Z – 283)
                           288 = 1.8*(Z – 273)
Make Z the subject:  288÷1.8 = Z – 273
                                     160 = Z – 273
                                     160 + 273 = Z ➡ Z = 433Kelvin

2. Convert 385K to temperature in degree Fahrenheit.

Solution:
Data given in the question:
Temperature in kelvin, Z = 385K
Formula:  DE/DF = GH/GI
                     (Y – 32)/(212 – 32) = (385 – 273)/(373 – 273)
Substitution:
                     (Y – 32)/180 = 112/100
.                    (Y – 32)/180 = 1.12
                      Y – 32 = 1.12*180
.                     Y – 32 = 201.6
                      Y = 201.6 + 32. ➡ Y = 233.6°F
Or
  You an use direct substitution as follow:
Temperature in Kelvin, Z = 385K
Formula:          Y – 32 = 1.8*(Z – 273)
Substitution:   Y – 32 = 1.8*(385 – 273)
                          Y – 32 = 1.8*112
                          Y – 32 = 201.6 ➡ Y = 201.6 + 32
                    ➡ Y = 233.6°F

Relationship Between Temperature in Degree Celsius and Kelvin:
The difference between temperature in degree Celsius and Kelvin is the formula that connect the two scales. The formula is as stated below.
Temperature in Kelvin T = temperature in degree Celsius @ + 273
That is,
                T = ( @ + 273 )K

Application Of Formula:
Worked Examples:
1. What is the value of 35°C in Kelvin?

Solution:
Data given in the question:
Temperature in degree Celsius = 35°C

Formula:       temperature in Kelvin = @ + 273
Substitution:        T n Kelvin = 35 + 273. ➡ T in kelvin = 308 Kelvin

2. Change 356K to temperature in degree Celsius

Solution:
Data given in the question:
Temperature in Kelvin = 356K
Formula:    Temperature in Kelvin = @ + 273
Substitution: 356 = @ + 273
Make @ the subject:    @ = 356 – 273   ➡ @ = 83°C

3. Convert – 120°C to temperature in Fahrenheit.

Solution:
Data given in the question:
Temperature in degree Celsius = -120°C
Formula:               Temperature in Kelvin = @ + 273
Substitution:       T in Kelvin = - 120 + 273.  ➡ T = 153 Kelvin

Determination Of Upper and Lower Fixed Points Of a Thermometer:

Determination of upper fixed point:
Aim:
To determine the upper fixed point of a thermometer.
Apparatus:
Double wall steam jacket, manometer, thermometer, heat source, water.

Setup Diagram:
The set up diagram is as shown by the figure.

Procedure:
Use a cork and suspend the thermometer in the steam jacket such that its bulb is above the water surface.
Attach a manometer to the steam jacket and use it to balance the pressure inside the steam jacket with atmospheric pressure by balancing the mercury levels in both arm of he  u-tube ,( I.e 760 mmHg).
Attach a steam outlet to the hypsometer to ensure that no steam condenses on the thermometer. Heat the water to boiling.
After some times, when the mercury thread is steady, mark the mercury level.

Observation:
The mercury thread rises to a steady level.

Conclusion:
The marked level of the mercury thread is the upper fixed point of the thermometer.

Precautions:
I. make sure that the thermometer bulb does not touch the water.
II. Mark the mercury level when the mercury thread is steady.
III. Make sure the pressure inside the hypsometer is balanced with the atmospheric pressure.
IV. Make sure a steam outlet is attached to the hypsometer so that no steam condenses on the thermometer.

Determination Of Lower Fixed Point:
Aim:
To determine the lower fixed point of a thermometer.

Apparatus:
Thermometer to be calibrated, ice block, funnel and conical flask.
Tetup Diagram:


Procedures:
Insert the thermometer vertically into ice locks contained in a funnel such that it is visible enough. After some times that the mercury level is steady, marks the mercury level.

Observation:
The mercury level falls gradually to a steady level.

Conclusion:
The marked mercury level is the lower fixed point of the thermometer.

Precautions:
I. Insert the thermometer such that the mercury thread is visible.
II. Mark the level when the mercury thread is steady.

Types Of Thermometers:
There are different types of thermometer based on their thermometric substances. They are:
I. Liquid – in – glass thermometer:
these are thermometers whose thermometric substances are liquids.

Types Of Liquid -in-glass thermometer:
1. Mercury – in – glass thermometer:
In mercury in glass thermometer, mercury is used as the thermometric substance.
2. Alcohol – in – glass thermometer:
In alcohol – in – glass thermometer, alcohol is used as the thermometric substance in making the thermometer.

How to increase The Sensitivity Of Liquid – in – glass thermometer:
I. Use thin bulb:
Thin bulb enable the liquid inside the bulb to detect any small change in temperature.
II. Use narrow capillary tube:
Narrow capillary enable small temperature to produce large increase in mercury thread or length.
III. Use liquid of high expansivity:
The liquid should expand great for any Small change in temperature.

Properties Of  Liquids  as Thermometric Substances :
Liquids that are used as thermometric substances should have the following properties:
I. The liquid should expand and contract uniformly with temperature
II. The liquid should have high boiling point
III. The liquid should have low melting point
IV. The liquid should be opaque and easily seen

Reasons That Water Is not Use As Thermometric Substance:
Water is not used as thermometric substance because of e following:
I. Water has small range of expansion.
II. Water freezes at 0°
III. Water boils at 100°
IV. Water does not expand uniformly ( of contract from 0°C to 4°C )
V. Water wet glass
VI. Water is colourless and make it difficult to read its meniscus.

Comparison of Mercury and Alcohol as Thermometric Substances:
I. Mercury has greater conductivity than alcohol. It expands rapidly. It indicate temperature chance quickly.
Alcohol has poor conductivity.  It expands slowly. It respond to temperature change slowly.
II. Mercury is opaque. It is easily seen.
Alcohol need to be coloured before it can be easily seen.
III. Mercury has convex meniscus and does not wet glass.
Alcohol has concave meniscus, clinch to the wall of the glass and wet the glass.
IV. Mercury does not vaporize easily.
Alcohol vaporize easily even at low temperature.
V. Mercury can be used to measure higher temperature. It boils at 357°C.
Alcohol cannot be used to measure higher temperature. It boils at 78°C.

Advantages Of Alcohol Over Mercury As A Thermometric Liquid:
I. Alcohol freezes at – 115°C while mercury freezes at -39°C
II. Alcohol can be used to measure very low temperature while mercury can not.
III. The expansivity of alcohol is about six times that of mercury for the same temperature rise.

II. Clinical Thermometer:
Clinical thermometer is a mercury in glass thermometer that is used in hospital to measure human body temperature. The temperature of a healthy normal human being is 37°C. The temperature may rise to 41°C when the person have high fever.
The temperature range of a clinical thermometer is between 35°C to 43°C.

Diagram:

Important Features Of Clinical Thermometer:
Clinical thermometer bore has a bend called kink or constriction. The constriction allow expanded mercury thread to flow and prevent the reflux of the mercury thread until the thermometer reading is taken. After the reading is taken, the thermometer is vigorously shaken to return the mercury into the bulb.

Sterilization Of Clinical Thermometer:
Clinical thermometer is not sterilized in boiling water at normal pressure because the thermometer has a small temperature range which does not extend to 100°C. At 100°C, the glass of the thermometer is forced to expand excessively, the glass will brake.

Maximum and Minimum Thermometer:
Maximum and minimum thermometer is a liquid in glass thermometer. It is used to measure and record the maximum and minimum temperature of the day. It is used by whether men in meteorological stations. The most common maximum and minimum thermometer is the six's combined maximum and minimum thermometer which was invented by James Six.

Construction Of Maximum And Minimum Thermometer:
Maximum and minimum thermometer is a U – shape stem that is connected to two bulbs X and Z. The two bulbs contain alcohol which are separated by a column of mercury in the u – bend. Bulb P is completely filled with alcohol while bulb  Q is partly filled so that some air space are provided at the top of the bulb. Two indexes float in the alcohol in both sides of the tube. Temperature scales are provided by the sides of the tube.

Diagram:

Principles Of Operation Of Maximum and Minimum Thermometer:
When temperature increases, the alcohol vapour expands and push the mercury round the thermometer. The mercury pushes index L1 up the tube and indicate the maximum temperature of the day.