Zeroth Law of Thermodynamics: Temperature Units Explained

Thermal expansion occurs when materials increase in size with temperature. Solids expand linearly (one dimension), superficially (two dimensions), or volumetrically (three dimensions). The variation equals initial dimension multiplied by the coefficient and temperature change. For liquids, apparent expansion differs from actual expansion because containers also expand. The apparent coefficient equals the liquid's coefficient minus the container's coefficient. All coefficients relate to the linear coefficient: superficial is twice, volumetric is three times.

Most substances expand when heated and contract when cooled, changing their dimensions. In solids, three types of thermal expansion occur: linear (ΔL/L = αLΔT), area (ΔA/A = 2αLΔT), and volume (ΔV/V = 3αLΔT) expansion, where αL is the coefficient of linear expansion—a material-specific constant. Different materials expand differently: metals expand more than glass or Pyrex. For liquids, the coefficient of volume expansion varies significantly, with ethyl alcohol having very high values. Mercury's moderate expansion makes it suitable for thermometers.

All materials expand when heated and contract when cooled. Solids expand when heated, demonstrated through metal ball and ring experiments where heated balls no longer fit through rings. Different solids expand at different rates: aluminum expands most, followed by copper, then iron. Liquids also expand when heated, shown through colored water in a flask with glass tube, where heating causes water level to rise. Different liquids expand at different rates: alcohol expands most, followed by oil, then water. This occurs because particles gain energy and move apart, increasing volume.

Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. When materials are heated, they expand, and when cooled, they contract. This phenomenon occurs in both solids and liquids. In solids, thermal expansion primarily affects length, while in liquids, it affects volume. The relationship between thermal expansion and temperature change is directly proportional, meaning that as temperature increases, the expansion increases proportionally. This principle is fundamental in physics and engineering, with practical applications in designing structures, measuring temperature with thermometers, and understanding material behavior under thermal stress.

Thermal expansion is the phenomenon where materials change dimensions when exposed to temperature changes. Linear expansion of solids depends on temperature change, original length, and material type. The coefficient of linear expansion (α) measures expansion per degree per meter. The formula L = L₀(1 + αΔT) calculates final length. Different materials have different coefficients: copper (17×10⁻⁶), iron (11.3×10⁻⁶), glass (4×10⁻⁶) /°C. Solids also expand in volume when heated. Liquids expand when heated, with apparent expansion depending on both liquid and container, while true expansion depends only on the liquid's nature.

The kinetic theory of gases explains gas behavior through five fundamental assumptions (RVAED): particles have negligible volume, move randomly in all directions, experience no attraction, undergo elastic collisions, and have brief collision durations. Starting with a single particle in a cubic container, the derivation shows how pressure arises from momentum changes during elastic collisions. Extending to many particles introduces root mean square speed (crms), leading to the key equation PV = (1/3)Nmc². This connects microscopic particle motion to macroscopic properties: pressure relates to density and speed squared, while average kinetic energy per particle equals (3/2)kT. Brownian motion—random movement of dust particles under microscope—provides experimental evidence confirming gas molecules undergo random motion, validating the kinetic theory framework.

The kinetic theory of gases explains macroscopic gas properties through microscopic molecular motion. Built on the atomic hypothesis, it derives the ideal gas law (PV = nRT) from molecular collisions. The derivation shows pressure results from molecules exerting force on container walls through elastic collisions. By analyzing momentum changes and collision frequencies, the theory reveals that temperature measures the average kinetic energy of molecules: (1/2)m<V²> = (3/2)kT. This provides the first microscopic interpretation of temperature, showing that thermometers measure molecular kinetic energy indirectly. The theory demonstrates how atomic hypothesis explains gas behavior and validates the existence of atoms through experimentally verifiable predictions.

The kinetic theory of gases explains gas behavior through molecular motion. Key assumptions include: gas molecules are in constant random motion in all directions, molecules are very small compared to their separation (treated as point particles), no intermolecular forces except during collisions, and collisions are perfectly elastic. Temperature represents the average kinetic energy of molecules, with higher temperature meaning faster molecular motion. The kinetic interpretation of temperature states that temperature is directly proportional to the average kinetic energy of molecules, given by (3/2)kT. The Maxwell-Boltzmann distribution describes how molecular speeds are distributed in a gas at a given temperature, showing most molecules have speeds near the average with fewer at extreme speeds. Temperature is the only factor affecting molecular speed, not gas type or mass. This fundamental relationship connects macroscopic temperature to microscopic molecular motion, explaining why gases behave as they do under different thermal conditions.

Microscopic structure determines macroscopic behavior. Solid particles occupy regular positions; liquid particles have random positions with distances ~particle size; gas particles have distances ~1000× larger. Molecular density of liquid water is ~3×10²⁸/m³; ideal gas at STP is ~2.7×10²⁵/m³—a ratio of ~10³. Mean free path: gas ~10⁷ m, liquid ~10⁻¹⁰ m. The kinetic theory derives gas pressure from molecular collisions: P=(1/3)nm̄u², showing pressure depends on molecular density, mass, and velocity squared. Temperature relates to average kinetic energy: ⟨KE⟩=(3/2)kBT for monatomic gases. This connects microscopic molecular motion to macroscopic temperature measurement.

Key kinetic theory equations include: v_rms = √(3RT/M), Pressure P = (1/3)nmv²_rms, Average kinetic energy per molecule = (3/2)kBT, Total internal energy of one mole of diatomic gas = (5/2)RT. Kinetic theory provides microscopic explanation for macroscopic properties: pressure results from momentum change of molecules colliding with container walls, and temperature relates to average translational kinetic energy. In elastic collisions, both momentum and kinetic energy are conserved.

Specific heat capacity (c) is the heat required to raise 1 unit mass by 1°C, given by Q = mcΔT. Molar specific heat capacity is for one mole of substance. Heat capacity is for the entire body. The principle of calorimetry states that heat lost by hot bodies equals heat gained by cold bodies. A calorimeter consists of a copper vessel (good conductor) containing water, with a thermometer. This principle allows measurement of specific heat capacities by mixing substances and measuring temperature changes. During phase changes, temperature remains constant while heat is absorbed or released. Latent heat of fusion is for melting/freezing, and latent heat of vaporization is for vaporization/condensation. The effect of pressure on phase changes includes: for most substances, increasing pressure increases melting point, but for water, increasing pressure decreases melting point (regelation). The boiling point increases with pressure. This explains why ice skates glide on ice and why pressure cookers work. To solve calorimetry problems: identify hot and cold bodies, apply the principle that heat lost equals heat gained, use Q = mcΔT for each substance, and solve for the unknown quantity.

Heat transfers from hotter to colder bodies. The principle of calorimetry states heat lost equals heat gained: m₁c₁ΔT₁ = m₂c₂ΔT₂. Specific heat capacity is heat required to raise 1 kg of substance by 1°C: c = Q/(mΔT). Water has the highest specific heat capacity (4200 J/kg·K), making it effective as a coolant. Latent heat is absorbed or released during phase changes without temperature change. Specific latent heat of fusion for ice is 334,000 J/kg. Heating curves show temperature rising until phase changes, where temperature remains constant despite heat absorption.

Specific heat capacity (c) is the heat required to raise 1 kg of substance by 1°C: Q = mcΔT. For water, c ≈ 4200 J/kg·°C. Latent heat is heat absorbed/released during phase change without temperature change. Latent heat of fusion (L_f = 334,000 J/kg for ice) melts solids, while latent heat of vaporization (L_v = 2,260,000 J/kg for water) vaporizes liquids. The principle of calorimetry states that in an isolated system, heat lost equals heat gained: Heat Lost = Heat Gained. The final equilibrium temperature lies between initial temperatures.

Heat capacity (C) equals mass times specific heat capacity (C = mc). It can also be calculated from heat and temperature change (C = Q/ΔT). Mass must be converted from grams to kilograms. The calorimetry law states Q = mcΔT for temperature changes without phase change. This allows calculation of heat gained or lost when substances are heated or cooled. For example, 200g water heated from 20°C to 80°C absorbs 50,400 J. For a fixed amount of heat added, temperature change is inversely proportional to mass and specific heat capacity. Smaller mass or lower specific heat capacity results in greater temperature increase.

Calorimetry is the science of measuring heat. Heat is a form of energy that flows from hot to cold bodies. The SI unit of heat is Joule, while calorie is the most commonly used unit (1 cal = 4.2 J). Temperature indicates the thermal state of a body and determines heat flow direction. Kelvin is the SI unit of temperature, with conversion: Kelvin = Celsius + 273. Heat capacity (C) is the heat required to raise a body's temperature by 1°C: C = Q/ΔT. Specific heat capacity (c) is the heat required to raise 1 kg of substance by 1°C: c = Q/(mΔT). The fundamental formula is Q = mcΔT. Water has the highest specific heat capacity (4200 J/kg·°C), followed by ice (2100 J/kg·°C) and copper (385 J/kg·°C).