Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Thermodynamics → Laws of Thermodynamics ↓


Zeroth law of thermodynamics


The study of thermodynamics involves understanding the flow of heat and how it affects matter. At the core of thermodynamics are several fundamental laws that determine the interaction of energy in the universe, one of which is the zeroth law of thermodynamics. Although it is less well known than the first, second, or third laws, the zeroth law is just as important to the foundations of thermodynamics. It provides a basis for the concept of temperature.

Understanding thermal equilibrium

Before we get into the zeroth law, we need to fully understand the concept of thermal equilibrium. Suppose you have two objects at different temperatures, say a hot cup of coffee and a cold ambient room. If you leave the cup of coffee on the table, over time it will lose heat to the air in the room, causing it to cool down. Conversely, the air in the room gains a little energy, causing it to become slightly warmer, but this change is usually negligible because rooms are much larger than cups of coffee.

This process continues until the coffee and the room eventually reach the same temperature – they achieve thermal equilibrium. Thermal equilibrium is the state where two objects in contact with each other stop exchanging heat because they reach the same temperature.

Zeroth law defined

Now that we understand thermal equilibrium, we can move on to the zeroth law of thermodynamics. The zeroth law states:

If two systems are in thermal equilibrium with a third system, they will also be in thermal equilibrium with each other.

In simple terms, this means that if system A is at the same temperature as system C, and system B is also at the same temperature as system C, then system A and system B must have the same temperature. This can be mathematically written as:

If A = C and B = C, then A = B

Now let's look at a visual example for clarification:

A B C

In this diagram, system A and system B are each in thermal equilibrium with system C. According to the zeroth law, system A and system B must be in thermal equilibrium with each other, even if they are not in direct contact. This principle is fundamental in defining what we mean by temperature.

Practical implications and applications

The zeroth law of thermodynamics is important because it allows us to use thermometers to measure temperature. To understand why, consider a simple example involving a thermometer. When you place a thermometer in a glass of water, the thermometer and the water interact until they reach thermal equilibrium. Since they are in equilibrium, they are at the same temperature, and thus, the thermometer measures the temperature of the water.

Example: Measuring room temperature

Imagine you want to measure the temperature of the air in your room. When you place a thermometer in the room, the mercury or alcohol inside the thermometer expands or contracts until it comes into thermal equilibrium with the air in the room. The reading on the thermometer gives the temperature of the room because of the zeroth law of thermodynamics.

Thus, if another object is in thermal equilibrium with the air in the room, such as a pillow on a sofa, and the thermometer reads 22°C, we can say with confidence that the pillow is also at 22°C.

Why is it called the "zero" rule?

Although the assumptions behind the zeroth law have long been implicit in thermodynamic theories, the law was relegated to secondary consideration after the first three laws were established. Scientists realized that a more fundamental understanding of temperature must precede the other laws, so they introduced the zeroth law as an initial foundational statement. Since it logically precedes the first law, it was called the zeroth law.

Historical context

The origins of the zeroth law can be traced back to the work of 19th-century scientists such as James Clerk Maxwell and Lord Kelvin. Much of the foundation for thermodynamics was laid at this time, as the study of heat and temperature began to be reconciled with classical mechanics and kinetic theory.

Development of understanding of heat

Initially, the study of heat revolved around calorimetry and the conservation of energy. Early thermodynamics dealt with work and energy conversion through processes such as the steam engine. This focus shifted toward understanding heat transfer and temperature in greater detail, leading to a broader understanding of how systems interact when isolated from external influences.

In your everyday life, the zeroth law is observed through various applications of temperature measurement, where instruments achieve equilibrium with the systems they measure. Once enthusiasts and observers such as Ludwig Boltzmann and Rudolf Clausius expanded on these concepts, the need for the zeroth law as an axiom became clear.

Visual example: The transitive nature of temperature

Consider three systems: a metal rod, a piece of ice, and a tub of hot water. The metal rod is immersed in the ice and comes to equilibrium; next, the same rod is placed in hot water and comes to equilibrium again.

metal rod snow hot water

Even though the rod never directly contacts both the ice and the hot water simultaneously, according to the zeroth law of thermodynamics, we know that at these successive equilibrium points, the ice and the hot water are effectively connected by thermal equilibrium through the rod.

Mathematical formulation

Let us consider three systems (A), (B), and (C). According to the zeroth law of thermodynamics, if system (A) is in thermal equilibrium with system (B), and system (B) is in thermal equilibrium with system (C), then system (A) is in thermal equilibrium with system (C). In terms of temperature, this can be expressed as:

T(A) = T(B) and T(B) = T(C) implies T(A) = T(C)

Here, (T(X)) denotes the temperature of the system (X).

Conclusion

The zeroth law of thermodynamics forms the foundation upon which the rest of thermodynamic theory is built. Without the understanding that different systems can equalize in temperature when no more heat flows between them, predicting the outcome of any form of energy transfer would remain intractable and unattainable.

While this premise may seem simple—just setting a common temperature—it is the first lens through which to view and understand the dynamic world of energy transfer. Whether for industrial applications, scientific explorations, or cooking a great meal, recognizing when a system reaches thermal equilibrium underlies both our theoretical knowledge and our practical experiences every day.


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Zeroth law of thermodynamics

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