Definition and Concept
Thermodynamic Quantity
Temperature: scalar physical quantity representing hotness or coldness. Measures average kinetic energy of particles in a system. Determines direction of heat flow. Fundamental parameter in thermodynamics.
Thermal State Indicator
Describes system's thermal energy distribution. Independent of system size or amount of substance. Enables comparison of thermal conditions between bodies.
Intensive Property
Temperature: intensive property. Does not scale with system size. Unlike energy or heat, remains constant on division of system.
Temperature Scales
Celsius Scale (°C)
Defined by water phase transitions: 0°C (ice melting), 100°C (water boiling) at 1 atm. Widely used in daily life and science. Interval scale, not absolute.
Fahrenheit Scale (°F)
Developed by Daniel Gabriel Fahrenheit, based on human body and freezing points. Ice melting at 32°F, water boiling at 212°F. Mainly used in USA and few countries.
Kelvin Scale (K)
Absolute temperature scale. Zero point: absolute zero (-273.15°C). Interval equal to Celsius degree. SI base unit for temperature. Used in scientific contexts.
Rankine Scale (°R)
Absolute scale using Fahrenheit degree increments. Zero at absolute zero. Primarily used in some engineering fields in the USA.
| Scale | Freezing Point of Water | Boiling Point of Water | Absolute Zero |
|---|---|---|---|
| Celsius (°C) | 0 | 100 | -273.15 |
| Fahrenheit (°F) | 32 | 212 | -459.67 |
| Kelvin (K) | 273.15 | 373.15 | 0 |
| Rankine (°R) | 491.67 | 671.67 | 0 |
Kinetic Theory and Temperature
Molecular Motion
Temperature proportional to average translational kinetic energy of particles. Higher temperature: faster molecular velocities. Equation links microscopic motion to macroscopic quantity.
Relation to Kinetic Energy
For ideal gases, average kinetic energy per molecule: (3/2)k_B T, where k_B is Boltzmann constant, T absolute temperature. Basis for thermodynamic temperature scale.
Microscopic Interpretation
Temperature reflects distribution of kinetic energies among particles. Maxwell-Boltzmann distribution describes velocity spread. Fluctuations exist but mean relates to temperature.
Thermal Equilibrium and Zeroth Law
Zeroth Law of Thermodynamics
If two systems are each in thermal equilibrium with a third system, they are in equilibrium with each other. Establishes temperature as transitive property.
Thermal Equilibrium Definition
No net heat flow between systems in contact. Implies equal temperature. Enables consistent temperature measurement and scale definition.
Implications for Measurement
Thermometer reaches thermal equilibrium with object measured. Reading stable and reproducible. Foundation for temperature as measurable physical quantity.
Absolute Zero and Thermodynamic Temperature
Definition of Absolute Zero
Lowest theoretical temperature where particle motion ceases (classical view). Defined as zero on Kelvin scale. Unattainable in practice but approached in laboratories.
Third Law of Thermodynamics
Entropy approaches constant minimum at absolute zero. Implies impossibility of reaching absolute zero exactly. Fundamental limit for cooling processes.
Significance in Thermodynamics
Provides absolute reference for temperature scales. Enables calculation of entropy and thermodynamic potentials. Crucial in cryogenics and quantum physics.
Temperature Measurement Methods
Contact Thermometry
Direct thermal contact between sensor and object. Includes liquid-in-glass, thermocouples, resistance thermometers. Requires thermal equilibrium for accuracy.
Non-contact Thermometry
Infers temperature from emitted radiation or other properties. Infrared thermometers, pyrometers. Useful for high temperatures or moving objects.
Thermodynamic Temperature Measurement
Based on fundamental laws and fixed points. Includes gas thermometers and acoustic methods. Provides traceability to SI units.
Types of Thermometers
Liquid-in-Glass Thermometers
Use expansion of liquid (mercury, alcohol) with temperature. Simple, robust, limited range and precision. Widely used in everyday applications.
Thermocouples
Based on Seebeck effect: voltage generated at junction of two metals varies with temperature. Wide range, fast response, requires calibration.
Resistance Temperature Detectors (RTDs)
Electrical resistance changes with temperature. Platinum RTDs common for precision. Stable, linear response over moderate temperature ranges.
Thermistors
Semiconductor resistors with high temperature sensitivity. Negative or positive temperature coefficient. Used in electronic circuits for control and measurement.
| Thermometer Type | Operating Principle | Temperature Range | Typical Applications |
|---|---|---|---|
| Liquid-in-Glass | Thermal expansion | -39°C to 357°C (mercury) | Environmental, medical |
| Thermocouple | Seebeck effect voltage | -200°C to 2300°C | Industrial, high-temp |
| RTD | Resistance change | -200°C to 850°C | Laboratory, process control |
| Thermistor | Resistance change | -50°C to 150°C | Electronics, medical |
Heat Transfer and Temperature
Heat Flow Direction
Heat flows spontaneously from higher to lower temperature. Temperature gradient drives heat transfer processes. Fundamental thermodynamic principle.
Modes of Heat Transfer
Conduction: molecular collisions transfer energy. Convection: bulk fluid motion. Radiation: electromagnetic waves. All depend on temperature differences.
Temperature Gradient
Spatial rate of temperature change. Determines local heat flux. Expressed as ∇T in vector calculus. Key factor in thermal conduction equations.
Statistical Thermodynamics Connection
Temperature as Statistical Parameter
Defined via entropy and internal energy relation: 1/T = ∂S/∂U at constant volume and particle number. Connects microscopic states with macroscopic observables.
Boltzmann Distribution
Probability of system in state i: P_i ∝ exp(-E_i/k_B T). Temperature governs population of energy states. Explains temperature-dependent phenomena.
Fluctuations and Equilibrium
Temperature stable in large systems, fluctuates in small systems. Statistical ensembles assume uniform temperature. Basis for thermodynamic equilibrium definitions.
Role of Temperature in Physics
Thermodynamics
Key variable in laws of thermodynamics. Determines state functions, phase transitions, reaction rates. Fundamental in defining entropy and free energy.
Condensed Matter Physics
Controls material properties: conductivity, magnetism, superconductivity. Temperature variation induces phase changes and critical phenomena.
Cosmology and Astrophysics
Describes thermal state of stars, cosmic microwave background. Temperature measurements reveal universe evolution and energy distributions.
Practical Applications
Industrial Processes
Temperature control critical in manufacturing, chemical reactions, metallurgy. Ensures product quality and safety.
Weather and Climate
Atmospheric temperature drives weather patterns, climate zones. Measured globally for forecasting and research.
Medical and Biological
Body temperature indicates health status. Controlled in incubators and cryopreservation. Essential in physiological studies.
Key Formulas
Average Kinetic Energy of Gas Molecules
E_{kin} = \frac{3}{2} k_B TConversion Between Celsius and Kelvin
T(K) = T(°C) + 273.15Heat Flow Rate by Conduction (Fourier’s Law)
Q = -k A \frac{dT}{dx}Boltzmann Distribution Probability
P_i = \frac{e^{-\frac{E_i}{k_B T}}}{Z}, \quad Z = \sum_j e^{-\frac{E_j}{k_B T}}References
- Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, Wiley, Vol. 2, 1985, pp. 45-78.
- Reif, F., Fundamentals of Statistical and Thermal Physics, McGraw-Hill, Vol. 1, 1965, pp. 120-150.
- Atkins, P.W., Physical Chemistry, Oxford University Press, 10th Ed., 2014, pp. 200-230.
- Tipler, P.A., Mosca, G., Physics for Scientists and Engineers, W.H. Freeman, 6th Ed., 2007, pp. 450-480.
- Feynman, R.P., Leighton, R.B., Sands, M., The Feynman Lectures on Physics, Addison-Wesley, Vol. 1, 1963, pp. 39-66.