Temperature Scales and Thermometers

Thermometry is the branch of physics that deals with the measurement of temperature. To measure temperature quantitatively, scientists utilize specific physical properties of matter that change continuously and predictably with temperature. These properties are known as thermometric properties.

Common Thermometric Properties

• Volume of a Liquid: Expands or contracts with temperature changes (used in mercury or alcohol-in-glass thermometers).
• Pressure of a Gas at Constant Volume: Increases linearly with temperature (used in constant-volume gas thermometers).
• Volume of a Gas at Constant Pressure: Increases linearly with temperature (used in constant-pressure gas thermometers).
• Electrical Resistance of a Metal: Changes with temperature (used in platinum resistance thermometers).
• Electromotive Force (EMF): Generated across the junctions of two dissimilar metals when kept at different temperatures (used in thermocouples).

Principle of Temperature Scales

To establish a temperature scale, two highly reproducible reference temperatures, known as fixed points, are chosen.

Standard Reference Points

• Lower Fixed Point (LFP): The freezing point or ice point, which is the temperature of pure melting ice at standard atmospheric pressure (1 atm).
• Upper Fixed Point (UFP): The boiling point or steam point, which is the temperature of pure boiling water or steam at standard atmospheric pressure (1 atm).

Core Temperature Scales

Temperature Scale	Symbol	Lower Fixed Point (LFP)	Upper Fixed Point (UFP)	Total Fundamental Intervals
Celsius Scale	°C	0°C	100°C	100 equal divisions
Fahrenheit Scale	°F	32°F	212°F	180 equal divisions
Kelvin Scale (Absolute)	K	273.15 K	373.15 K	100 equal divisions
Rankine Scale	°Ra	491.67 °Ra	671.67 °Ra	180 equal divisions
Reaumur Scale	°R	0°R	80°R	80 equal divisions

Universal Inter-conversion Formula

Any temperature reading (T) on a given scale can be converted to another scale using the fundamental linear relationship:

Applying this rule to the most common scales yields the standard equation: This can be simplified for quicker calculations:

Core Temperature Observations

• Equality Point for Celsius and Fahrenheit: The Celsius and Fahrenheit scales read the exact same numerical value at -40° (i.e., -40°C = -40°F).
• Equality Point for Fahrenheit and Kelvin: The Fahrenheit and Kelvin scales register the same numerical value at $574.25$ (i.e., 574.25°F = 574.25 K).

Types of Thermometers and Industrial Applications

Different thermometers are constructed based on different thermometric properties to suit specific temperature ranges and accuracy requirements.

Liquid-in-Glass Thermometers

• Mercury Thermometer: Mercury is preferred because it remains liquid over a wide temperature range, does not stick to glass, is an excellent conductor of heat, and has a uniform thermal expansion. It measures temperatures from -39°C to 350°C (its boiling point can be extended to 500°C by filling the upper space with pressurized nitrogen gas).
• Alcohol Thermometer: Alcohol has a very low freezing point (-115°C), making it highly suitable for measuring extreme cold in polar regions. However, it cannot measure high temperatures due to its low boiling point (78°C).

Gas Thermometers

Gas thermometers are highly accurate and are primarily used to calibrate other thermometers. They operate based on ideal gas laws.

• Constant-Volume Gas Thermometer: Uses hydrogen gas for temperatures from -200°C to 500°C, and helium gas for ultra-low temperatures down to -268°C.
• Limitation: They are bulky, slow to respond, and structurally complex, making them unsuitable for routine clinical or industrial use.

Resistance Thermometers (Platinum Resistance Thermometer)

• Working Principle: Based on the fact that the electrical resistance (R) of a pure metal increases linearly with temperature, given by the formula R_t = R₀(1 + α t).
• Range: It is extremely accurate over a vast range from -200°C to 1200°C.

Thermoelectric Thermometers (Thermocouples)

• Working Principle: Operates on the Seebeck Effect. When two junctions of two dissimilar metals (like iron and copper) are kept at different temperatures, an electromotive force (EMF) is generated across them. This EMF is directly proportional to the temperature difference.
• Range: Measures rapidly fluctuating temperatures from -200°C to 1600°C.

Pyrometers (Radiation Thermometers)

• Working Principle: Based on the Stefan-Boltzmann Law (E ∝ T⁴). It measures the temperature of a body by detecting the intensity of the total electromagnetic radiation emitted by it, without making physical contact.
• Range: Used exclusively for high temperatures above 800°C up to several thousand degrees (e.g., measuring the temperature of molten metals in furnaces or the surface of stars). Below 800°C, bodies do not emit sufficient visual or infrared radiation for accurate detection.

Advanced Thermodynamic Standards

The Modern Definition of Kelvin

Historically, the Kelvin scale was defined relative to the Triple Point of Water. However, in May 2019, the International System of Units (SI) redefined the Kelvin by fixing the exact numerical value of the Boltzmann constant (k) to 1.380649 × 10^-23 J·K^-1. This anchored the definition of temperature directly to microscopic thermal energy rather than a specific material property of water.

Triple Point of Water vs. Ice Point

• The Ice Point (0°C): It is the melting point of pure ice at standard atmospheric pressure, measured in an environment exposed to air.
• The Triple Point of Water (0.01°C or 273.16 K): It is the precise temperature at which pure solid ice, liquid water, and water vapor coexist in stable thermodynamic equilibrium under a specific pressure of 611.657 Pa (0.006 atm) in a vacuum. It is preferred as a foundational standard because it is completely unaffected by ambient air pressure variations.

Clinical Thermometer Design Facts

A clinical thermometer is specifically designed to measure human body temperature.

• Range: It has a limited range from 35°C to 42°C (or 95°F to 110°F).
• The Kink/Constriction: It features a sharp narrow constriction (kink) in the capillary tube just above the bulb. This constriction prevents the mercury column from dropping spontaneously when the thermometer is removed from the patient’s mouth, allowing accurate reading. The mercury must be shaken down manually before the next use.

Last Modified: May 28, 2026