Temperature, heat transfer and changes of state

Temperature, heat transfer and changes of state

Temperature and internal energy

Temperature describes the thermal state of a body and determines the direction of spontaneous heat transfer when bodies can exchange energy. Internal energy includes microscopic kinetic and potential contributions. Heat refers to energy transferred because of a temperature difference, not a substance stored inside an object. A large container of warm water can have a larger internal-energy change for a given temperature fall than a small cup of hotter water. Mass, material and temperature change all matter. When two bodies reach thermal equilibrium there is no net heat transfer between them, although microscopic interactions continue. Distinguish temperature from the amount of transferred energy.

Thermometers and scales

A thermometer uses a reproducible temperature-dependent property, such as liquid volume, electrical resistance or thermoelectric emf. Fixed points and calibration connect that property to a scale. For a linear thermometer, the fractional change in the property corresponds to the fractional temperature change between calibration points. Celsius and kelvin intervals are equal in size, with. A rise of10°C is a rise of10 K, but10°C is a temperature of283.15 K. Kelvin has no degree sign. Gas calculations require absolute temperature, not an unconverted Celsius reading. Choose a thermometer appropriate to range, response and required precision rather than assuming one device suits every experiment.

Specific heat capacity

Specific heat capacity c is energy needed per kilogram per kelvin rise for the stated process without phase change. assumes c is effectively constant over the interval. Water's high specific heat capacity helps explain coolant applications and thermal moderation by large water bodies. High c does not mean faster heating under equal mass and input power; more energy is needed for the same rise. Heat capacity of a particular body is in J/K, different from specific heat capacity in J/(kg K). Electrical energy input can be VIt or Pt, but energy entering the heater is not necessarily all transferred to the sample.

Calorimetry and mixing

For an adequately insulated mixing calculation, energy lost by hotter parts equals energy gained by colder parts. With two water samples, provided no phase change or omitted container energy is significant. Include the calorimeter's heat capacity if supplied. In an ordinary no-phase-change mixing problem, final temperature should lie between initial temperatures. An answer outside that interval suggests a sign, algebra or modelling error. Write each temperature fall and rise as a positive difference to simplify the first energy account. If samples have different c values they do not cancel, so equal masses need not give the arithmetic-mean temperature.

Latent energy and heating curves

At a phase change under fixed pressure, energy can change molecular arrangement and separation without raising temperature. Specific latent heat L is energy per kilogram for that specified change. Fusion refers to melting or freezing, vaporisation to liquid–gas change. A heating curve has sloping regions during temperature rises and approximately level regions during ideal phase changes. Ice becoming warm water may need separate ice-warming, melting and water-warming calculations. A level temperature does not imply zero energy input. During cooling and freezing the corresponding energy transfers reverse. Use the appropriate latent heat for the named substance and transition rather than assuming all melting and boiling values are equal.

Evaporation and boiling

Evaporation occurs at a surface over a temperature range when some molecules escape. Higher temperature, greater surface area, airflow and lower surrounding humidity generally speed it under suitable conditions. Escaping molecules can remove more than average energy, cooling what remains unless energy is supplied. Boiling occurs throughout a liquid when vapour bubbles can persist under external pressure. Lowering pressure usually lowers boiling temperature. Extra heating power at a fixed-pressure boiling point can increase the vaporisation rate without an immediate further temperature rise. Dissolved substances can alter boiling or freezing behaviour, so a fixed100°C rule applies only under the stated water-purity and pressure assumptions.

Conduction, convection and radiation

Conduction transfers energy through microscopic interactions without bulk transport of the material. Mobile electrons contribute strongly in metals. Convection involves fluid movement, often driven by density differences or a mechanical device. A warmed fluid commonly expands and rises in gravity while cooler material replaces it. Radiation transfers electromagnetic energy and requires no medium. All bodies emit thermal radiation; net transfer depends on surfaces, temperatures and surroundings. Dark matte surfaces are generally strong absorbers and emitters under comparable conditions, while polished reflective surfaces reduce radiative transfer. A vacuum removes material transport across a gap but does not block radiation, explaining the multiple features needed in a vacuum flask.

Expansion in solids and liquids

For a small interval, a solid's linear expansion is. In a uniform isotropic solid, approximate area and volume coefficients are2α and3α. Expansion gaps protect structures, and bimetallic strips bend because bonded materials expand differently. Liquids have volume expansion, while water behaves anomalously between0°C and about4°C before ordinary expansion becomes dominant. When a liquid is heated in an expanding container, apparent expansion is the extra overflow relative to the container. Approximately γreal for compatible volume coefficients. The container's changing volume must be included if the question asks true liquid expansion. Heating does not create extra mass.

Heat-transfer calculations and experiments

For steady one-dimensional conduction through a uniform slab, power transfer is approximately kAΔT/L with suitable boundary conditions, where k is thermal conductivity. A thicker insulator reduces transfer at the same temperature difference, area and material. In heating experiments, control mass, initial temperature, container and power; stir when appropriate and keep the thermometer clear of direct heater contact. A lid, insulation and a reasoned allowance for container heat capacity improve calorimetry. Newton's law of cooling approximates cooling rate proportional to temperature excess over surroundings for a suitable range. It is a model with conditions, not an exact description of every radiating object at any temperature.

Self-check and applications

Heating0.50 kg water by20 K with. An ideal500 W heater supplies this in84 s; longer actual time can reflect losses. Melting0.10 kg ice at its melting point with without a temperature rise. A2 m rod with. In a sea breeze, land heating and density-driven circulation help explain near-surface airflow; compare day and night rather than treating wind as heat conduction. First classify a problem as temperature change, phase change, expansion or transfer rate, then select c, L, α or conductivity accordingly.