Temperature

Table of Contents
1. Zeroth law of thermodynamics
2. Thermometers and thermometric properties
3. Thermometer types and typical temperature ranges
4. Temperature - Definition and Concept
5. Common temperature scales and relations
6. Example: Converting temperature scales
7. Calibration, accuracy and selection of thermometers
8. Practical applications
9. Summary
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Zeroth law of thermodynamics

• The zeroth law states that if two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
• This law establishes the concept of thermal equilibrium and provides the basis for comparing temperatures of different bodies.
• The zeroth law is the foundational principle that makes practical temperature measurement possible by allowing the use of a thermometer (the third system) to compare two systems.

Thermometers and thermometric properties

Different types of thermometers rely on different thermometric properties - measurable physical quantities that change with temperature. Common pairings are shown below.

• Thermocouples commonly use combinations such as copper-constantan, and alloy pairs like chromel-alumel, and noble metal combinations involving platinum and rhodium.

Remarks on gas thermometers

• A constant-volume gas thermometer measures temperature from the pressure of a fixed mass of gas at fixed volume; for an ideal gas at constant volume, pressure is proportional to absolute temperature.
• A constant-pressure gas thermometer measures temperature from the volume change of a gas kept at constant pressure; for an ideal gas at constant pressure, volume is proportional to absolute temperature.

Thermometer types and typical temperature ranges

The practical useful range of measuring instruments varies. Typical ranges for some instruments are:

Short notes on listed devices

• Platinum resistance thermometers (PRTs) exploit the nearly linear change of platinum resistance with temperature; they are precise and stable for laboratory and industrial use.
• Thermocouples produce an EMF that depends on the temperature difference between two junctions; they are rugged and suitable for wide ranges and high temperatures.
• Radiation and optical pyrometers measure temperature by detecting electromagnetic radiation emitted by a body; they are used for very high temperatures and non-contact measurement.
• Segar cone is used to assess high temperature exposure (for example, in furnaces or ovens) in a simple, qualitative way over the stated range.
• Gas thermometers are accurate and are used as primary standards, especially in calibration laboratories.

Temperature - Definition and Concept

Temperature is a physical quantity that indicates the degree of hotness or coldness of a body. It is a measure of the average translational kinetic energy of the particles in a substance in classical thermodynamics and statistical mechanics.

Thermodynamic temperature scale

• A thermodynamic temperature scale is independent of the particular thermometric substance; it assigns an absolute temperature to a system based on fundamental thermodynamic principles.
• The SI unit of thermodynamic temperature is the kelvin (K).
• Absolute zero is the lower limit of the thermodynamic temperature scale; at absolute zero the thermal motion of particles reaches its minimum.

Common temperature scales and relations

Several temperature scales are in common use. Relations between them are used for conversion.

• The kelvin scale (K) is related to the Celsius scale (°C) by:
  T(K) = T(°C) + 273.16
• The Rankine scale (R) is related to the Fahrenheit scale (°F) by:
  T(R) = T(°F) + 459.67
• The Rankine and kelvin scales are related by:
  T(R) = 1.8 × T(K)
• The relation between Celsius and Fahrenheit is:
  T(°F) = 1.8 × T(°C) + 32
• Relations for temperature differences are:
  ΔT(°F) = 1.8 × ΔT(K) = ΔT(R)

Notes on the presented constants

• The constant 273.16 used above corresponds to the relation as given in the reference information provided; users should note that some references use 273.15 as the conversion constant between °C and K. Use the constant required by the examining or calibration standard being followed.

Example: Converting temperature scales

Example: Convert 100°C into kelvin, Fahrenheit and Rankine. Show work step-by-step.

Calibration, accuracy and selection of thermometers

• Calibration: Thermometers should be calibrated against primary standards (for example, a gas thermometer or fixed-point cells) to ensure accuracy.
• Accuracy and range: Select a thermometer with a suitable range and resolution for the application; accuracy often decreases near the extremes of the instrument's range.
• Response time and environment: Choose non-contact devices (pyrometers) for moving or hostile environments; choose contact devices (PRT, thermocouple, mercury-in-glass) for steady and accessible measurements.
• Sources of error: Errors arise from heat losses, poor thermal contact, radiation effects, self-heating (in electrical sensors), and calibration drift.

Practical applications

• Industrial process control uses thermocouples and resistance thermometers for temperature monitoring and regulation.
• Calibration laboratories use gas thermometers and fixed-point cells to maintain primary temperature standards.
• High temperature measurements in furnaces, metallurgy and glass production use radiation and optical pyrometers.
• Everyday applications use mercury-in-glass or digital thermometers for weather, clinical and household uses.

Summary

Temperature is a fundamental physical quantity indicating hotness or coldness. The zeroth law defines thermal equilibrium and enables temperature measurement. A variety of thermometers exploit different thermometric properties; the choice depends on required range, accuracy and environment. Common temperature scales (Celsius, kelvin, Fahrenheit and Rankine) are related by simple linear formulae used for conversions and for expressing absolute temperatures in thermodynamic calculations.