Table of Contents
Temperature Scales and Thermometry
1. Introduction
Temperature measurement is essential in science, medicine, engineering, meteorology and everyday life. Different temperature scales have been developed to express thermal conditions numerically.
The three principal temperature scales are:
- Celsius scale
- Fahrenheit scale
- Kelvin scale
Thermometry is the science of measuring temperature using instruments called thermometers.
Accurate temperature measurement requires an understanding of temperature scales, fixed reference points, calibration and the physical properties used by measuring instruments.
2. Celsius Temperature Scale
The Celsius scale is widely used in everyday life, laboratories and scientific applications.
At standard atmospheric pressure:
- Pure ice melts at approximately 0°C.
- Pure water boils at approximately 100°C.
The interval between these two reference temperatures is divided into 100 equal parts.
Each division represents one degree Celsius.
The Celsius symbol is °C.
2.1 Important Celsius Temperatures
| Physical condition | Temperature |
|---|---|
| Freezing point of water | 0°C |
| Normal human body temperature, approximate | 37°C |
| Room temperature, approximate | 20°C to 25°C |
| Boiling point of water | 100°C |
The boiling and freezing points depend on pressure and purity. The familiar values refer to approximately standard atmospheric pressure.
3. Fahrenheit Temperature Scale
The Fahrenheit scale is used in some countries, particularly the United States, for everyday temperature reporting.
At standard atmospheric pressure:
- Water freezes at 32°F.
- Water boils at 212°F.
The interval between these points is divided into 180 equal parts.
The Fahrenheit symbol is °F.
3.1 Celsius and Fahrenheit Relationship
The conversion equation is:
[
F=\frac{9}{5}C+32
]
Where:
- (F) = temperature in Fahrenheit
- (C) = temperature in Celsius
To convert Fahrenheit into Celsius:
[
C=\frac{5}{9}(F-32)
]
3.2 Important Fahrenheit Temperatures
| Physical condition | Temperature |
|---|---|
| Freezing point of water | 32°F |
| Normal human body temperature, approximate | 98.6°F |
| Boiling point of water | 212°F |
4. Kelvin Temperature Scale
The Kelvin scale is the SI thermodynamic temperature scale and is widely used in physics, chemistry and scientific calculations.
Unlike Celsius and Fahrenheit, Kelvin is an absolute temperature scale.
Its zero point is absolute zero, the lowest possible thermodynamic temperature.
The symbol is K, not °K.
4.1 Absolute Zero
Absolute zero is:
[
0\ \text{K}=-273.15^\circ\text{C}
]
At absolute zero, a system is in its lowest possible thermodynamic energy state. Quantum mechanical effects mean that particles are not necessarily motionless in the classical sense.
4.2 Kelvin and Celsius Relationship
The conversion formula is:
[
K=C+273.15
]
To convert Kelvin into Celsius:
[
C=K-273.15
]
4.3 Water Reference Points on the Kelvin Scale
| Physical condition | Temperature |
|---|---|
| Freezing point of water | 273.15 K |
| Boiling point of water | 373.15 K |
| Absolute zero | 0 K |
5. Comparison of Temperature Scales
| Feature | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Symbol | °C | °F | K |
| Freezing point of water | 0°C | 32°F | 273.15 K |
| Boiling point of water | 100°C | 212°F | 373.15 K |
| Absolute zero | −273.15°C | −459.67°F | 0 K |
| Common use | Everyday and scientific | Everyday in some countries | Scientific and thermodynamic calculations |
6. Combined Temperature Conversion Formula
The relationship between Celsius, Fahrenheit and Kelvin can be expressed as:
[
\frac{C}{5}=\frac{F-32}{9}=\frac{K-273.15}{5}
]
This relationship is useful for converting corresponding temperature readings between the three scales.
The direct conversion formulas are generally easier to use in numerical problems.
7. Temperature Intervals and Temperature Readings
A temperature reading indicates a particular temperature point, while a temperature interval indicates the difference between two temperatures.
The sizes of the Celsius and Kelvin divisions are identical.
Therefore:
[
1\ \text{K interval}=1^\circ\text{C interval}
]
However, the Fahrenheit division is smaller.
[
1^\circ\text{C interval}=1.8^\circ\text{F interval}
]
For example, an increase from 20°C to 30°C is an increase of 10°C, equivalent to an increase of 18°F.
When calculating temperature differences, the 273.15 offset between Celsius and Kelvin is not added.
8. Thermometry
Thermometry is the science and practice of measuring temperature.
An instrument used to measure temperature is called a thermometer.
Thermometers operate by detecting changes in physical properties that vary with temperature.
These properties are known as thermometric properties.
9. Thermometric Properties
A thermometric property is a measurable physical property that changes in a predictable way with temperature.
Important examples include:
9.1 Volume of a Liquid
Liquids such as mercury and coloured alcohol expand when heated and contract when cooled.
This property is used in liquid-in-glass thermometers.
9.2 Electrical Resistance
The electrical resistance of many conductors changes with temperature.
Resistance thermometers use this property to measure temperature.
9.3 Thermoelectric Voltage
When two different conductors form a thermocouple, a temperature difference between their junctions produces an electromotive force.
This voltage can be used to determine temperature.
9.4 Gas Pressure
The pressure of a gas at constant volume changes with temperature.
This property can be used in gas thermometers.
9.5 Thermal Radiation
Hot objects emit electromagnetic radiation. The intensity and spectral distribution of this radiation vary with temperature.
Infrared thermometers and optical pyrometers use this principle.
10. Types of Thermometers
10.1 Liquid-in-Glass Thermometer
A liquid-in-glass thermometer contains a liquid inside a narrow glass tube.
When the temperature increases, the liquid expands and rises in the capillary tube.
Common thermometer liquids include:
- Mercury
- Coloured alcohol
Advantages:
- Simple construction.
- No external power supply required.
- Easy visual reading.
Limitations:
- Fragile glass construction.
- Limited temperature range.
- Mercury presents toxicity and environmental hazards if released.
10.2 Clinical Thermometer
A clinical thermometer is designed to measure human body temperature.
Traditional clinical thermometers often use a constriction to retain the maximum reading temporarily.
Modern clinical thermometers are commonly digital.
The measurement range varies by design. Many conventional clinical thermometers cover approximately 35°C to 42°C.
10.3 Laboratory Thermometer
A laboratory thermometer is used to measure temperatures in scientific experiments.
It is generally designed for a wider temperature range than a conventional clinical thermometer.
10.4 Digital Thermometer
Digital thermometers use electronic temperature sensors and display readings numerically.
Advantages include:
- Easy reading.
- Rapid measurement in many designs.
- No mercury.
- Convenient use in medicine and laboratories.
10.5 Resistance Thermometer
Resistance thermometers measure temperature by detecting changes in electrical resistance.
Platinum resistance thermometers are widely used because platinum has stable and predictable electrical properties.
10.6 Thermocouple
A thermocouple consists of two dissimilar conductors joined to form measuring junctions.
A temperature difference produces a voltage that can be measured and converted into a temperature reading.
Thermocouples are commonly used in industrial furnaces, engines and manufacturing equipment.
10.7 Infrared Thermometer
An infrared thermometer estimates temperature by detecting thermal radiation emitted by an object.
It can measure temperature without direct physical contact.
Applications include:
- Medical temperature screening.
- Industrial equipment inspection.
- Food processing.
- Electrical maintenance.
10.8 Pyrometer
A pyrometer measures high temperatures, often without physical contact.
Optical and radiation pyrometers are used in furnaces, metal processing and other high-temperature environments.
11. Fixed Points and Calibration
Calibration is the process of comparing an instrument’s readings with known reference standards and adjusting or documenting its performance.
Traditional temperature calibration uses fixed reference points.
Examples include:
- Ice point of water.
- Steam point of water under specified pressure conditions.
Modern temperature standards are based on the International Temperature Scale and fundamental physical measurements.
11.1 Importance of Calibration
Calibration helps ensure:
- Reliable readings.
- Consistency between instruments.
- Accurate laboratory measurements.
- Quality control in industrial processes.
- Safety in temperature-sensitive operations.
12. Characteristics of a Good Thermometer
12.1 Accuracy
Accuracy describes how close a measured value is to the true or accepted reference value.
12.2 Precision
Precision describes the closeness of repeated measurements to one another.
An instrument can produce highly consistent readings while still having a systematic error.
12.3 Sensitivity
Sensitivity describes how much the instrument’s output changes for a given change in temperature.
12.4 Range
Range is the interval of temperatures that an instrument can measure reliably.
12.5 Response Time
Response time is the time required for an instrument to respond to a change in temperature.
12.6 Linearity
Linearity describes how closely an instrument’s output follows a straight-line relationship with temperature over its specified range.
13. Worked Examples
Example 1: Convert 25°C into Kelvin
Using:
[
K=C+273.15
]
[
K=25+273.15
]
[
\boxed{K=298.15\ \text{K}}
]
Example 2: Convert 25°C into Fahrenheit
Using:
[
F=\frac{9}{5}C+32
]
[
F=\frac{9}{5}(25)+32
]
[
F=45+32
]
[
\boxed{F=77^\circ\text{F}}
]
Example 3: Convert 98.6°F into Celsius
Using:
[
C=\frac{5}{9}(F-32)
]
[
C=\frac{5}{9}(98.6-32)
]
[
C=\frac{5}{9}(66.6)
]
[
\boxed{C=37^\circ\text{C}}
]
Example 4: Convert 300 K into Celsius
[
C=K-273.15
]
[
C=300-273.15
]
[
\boxed{C=26.85^\circ\text{C}}
]
Example 5: Convert a Temperature Increase of 15°C into Fahrenheit
For temperature intervals:
[
\Delta F=\frac{9}{5}\Delta C
]
[
\Delta F=\frac{9}{5}\times15
]
[
\boxed{\Delta F=27^\circ\text{F}}
]
14. Common Examination Mistakes
- Writing °K instead of K.
- Forgetting to subtract 32 when converting Fahrenheit into Celsius.
- Adding 273.15 when converting Celsius into Kelvin but incorrectly applying it to temperature differences.
- Confusing accuracy with precision.
- Assuming every thermometer uses liquid expansion.
- Treating absolute zero as a temperature that can be reached by ordinary cooling.
- Ignoring the effect of pressure on the boiling point of water.
36 Key Takeaways for Exams
- Thermometry is the science of measuring temperature.
- The three commonly discussed temperature scales are Celsius, Fahrenheit and Kelvin.
- The Celsius scale uses the freezing and boiling points of water as familiar reference points.
- Water freezes at approximately 0°C under standard atmospheric pressure.
- Water boils at approximately 100°C under standard atmospheric pressure.
- Water freezes at 32°F on the Fahrenheit scale.
- Water boils at 212°F on the Fahrenheit scale.
- The Kelvin scale is the SI thermodynamic temperature scale.
- Kelvin is an absolute temperature scale.
- The symbol for kelvin is K, not °K.
- Absolute zero is 0 K.
- Absolute zero is equivalent to −273.15°C.
- The conversion from Celsius to Kelvin is (K=C+273.15).
- The conversion from Kelvin to Celsius is (C=K-273.15).
- The conversion from Celsius to Fahrenheit is (F=\frac{9}{5}C+32).
- The conversion from Fahrenheit to Celsius is (C=\frac{5}{9}(F-32)).
- A temperature interval of 1 K equals an interval of 1°C.
- A temperature interval of 1°C equals an interval of 1.8°F.
- Thermometers measure temperature using thermometric properties.
- Liquid expansion is used in liquid-in-glass thermometers.
- Electrical resistance changes with temperature.
- Platinum is commonly used in resistance thermometers.
- Thermocouples operate through the thermoelectric effect.
- Infrared thermometers measure thermal radiation without direct contact.
- Pyrometers are used for measuring high temperatures.
- Clinical thermometers are designed for measuring body temperature.
- Laboratory thermometers are used in scientific experiments.
- Calibration compares instrument readings with known standards.
- Accuracy refers to closeness to the true or accepted value.
- Precision refers to consistency among repeated measurements.
- Sensitivity describes the response of an instrument to temperature changes.
- Range refers to the temperatures an instrument can measure reliably.
- Response time indicates how quickly a thermometer reacts to temperature changes.
- The boiling point of water varies with atmospheric pressure.
- The Celsius and Kelvin scales have equal-sized temperature intervals.
- Accurate temperature measurement is essential in medicine, science, engineering and industry.