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Thermal Physics

Introduction

Thermal Physics studies how large collections of particles behave when energy is transferred, stored, and transformed. In Grades 11–13, you can connect the microscopic motion of atoms and molecules with macroscopic quantities such as temperature, pressure, internal energy, and entropy. This course combines ideas from thermodynamics, kinetic theory, statistical physics, and heat transfer.

By the end of the course, you should be able to distinguish temperature from heat, use energy equations quantitatively, explain phase changes, apply the ideal gas law, interpret molecular-speed distributions, use the first and second laws of thermodynamics, estimate heat-engine efficiency, and relate thermal radiation to temperature.

The Kelvin scale is especially important in thermal physics because thermodynamic temperature is measured from absolute zero. Temperature differences have the same numerical size in kelvins and degrees Celsius, while their zero points differ by 273.15.

Temperature and Thermal Equilibrium

Macroscopic and Microscopic Views

Temperature is a macroscopic state variable. In a simple ideal gas, a higher thermodynamic temperature corresponds to a higher average translational kinetic energy of the particles. Temperature is not the total internal energy of a system: two objects can have the same temperature but very different masses and therefore very different internal energies.

The zeroth law of thermodynamics provides the basis for temperature measurement. If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other. At thermal equilibrium there is no net heat transfer between the systems.

For conversions between Celsius temperature and thermodynamic temperature, use $T / K = θ /^{\circ} C + 273.15$ . In gas laws and formulas such as the Carnot-efficiency equation, use kelvins.

Absolute Zero

Absolute zero is 0 K, equivalent to −273.15 °C. It is the lower limit of thermodynamic temperature. It should not be described as a point at which every microscopic motion must literally stop: quantum systems can retain zero-point energy even at 0 K.

Heat, Internal Energy, and Heat Transfer

Internal energy is the total microscopic energy associated with the particles of a system, including microscopic kinetic and potential contributions. Heat is energy transferred because of a temperature difference. Heat is therefore a transfer process, not a substance stored inside an object.

For a temperature change without a phase change, the energy transferred can often be modeled by:

$Q = m c Δ T$

where $Q$ is energy transferred in joules, $m$ is mass in kilograms, $c$ is specific heat capacity in joules per kilogram kelvin, and $Δ T$ is the temperature change.

Conduction, Convection, and Radiation

Conduction transfers energy through microscopic interactions within matter. In metals, mobile electrons can make conduction particularly effective. Convection transfers energy through the bulk motion of a fluid, often driven by density differences. Radiation transfers energy by electromagnetic waves and does not require matter.

When you compare insulation materials, separate the mechanisms carefully. A vacuum suppresses conduction and convection by matter, but radiation can still cross the gap. Reflective surfaces can reduce radiative transfer.

Phase Changes and Latent Heat

During a phase change at fixed pressure, energy can be transferred while the temperature remains approximately constant. The transferred energy changes the arrangement and interactions of particles rather than raising the temperature.

For a phase change, use:

$Q = m L$

where $L$ is the specific latent heat. For melting or freezing, use the latent heat of fusion. For boiling or condensing, use the latent heat of vaporization.

Fehler beim Erstellen des Vorschaubildes:

A phase diagram shows which phase is stable at different temperatures and pressures. Water has a triple point where solid, liquid, and vapor can coexist in equilibrium, and a critical point beyond which the liquid-gas distinction disappears.

Datei:Heating curve blank labelled exam.svg

A heating curve can include sloped sections, where temperature changes, and flatter regions, where a phase change absorbs energy. Real experiments may deviate from an idealized graph because of heat loss, imperfect insulation, pressure changes, and measurement delay.

Kinetic Theory and Ideal Gases

The kinetic theory explains gas pressure as the macroscopic result of particle collisions with container walls. For a dilute ideal gas, particles are treated as point-like compared with their separation, intermolecular forces are neglected except during collisions, and collisions are modeled as elastic.

Datei:Brownian motion.svg

Brownian motion provides visible evidence of microscopic molecular motion: a small suspended particle follows an irregular path because countless molecular collisions do not cancel perfectly at every instant.

Ideal Gas Law

The state of an ideal gas is related by:

$p V = n R T$

where $p$ is pressure, $V$ is volume, $n$ is amount of substance in moles, $R$ is the molar gas constant, and $T$ is thermodynamic temperature.

Fehler beim Erstellen des Vorschaubildes:

At constant temperature, Boyle's law gives $p V = c o n s t a n t$ . At constant pressure, Charles's law gives $V / T = c o n s t a n t$ . At constant volume, pressure is proportional to thermodynamic temperature for a fixed amount of ideal gas.

Datei:Boyles Law.svg

Molecular Energy and Speed Distributions

For a monatomic ideal gas in three dimensions, the mean translational kinetic energy per particle is:

$⟨ E_{k} ⟩ = \frac{3}{2} k_{B} T$

where $k_{B}$ is the Boltzmann constant. This relation links the microscopic particle model directly with thermodynamic temperature.

Gas molecules do not all move at the same speed. Their speeds form a distribution. As temperature increases, the Maxwell-Boltzmann distribution broadens and its most probable speed shifts to higher values.

Datei:Maxwell-Boltzmann-Distribution-simple-axis-labels.svg

This distribution helps explain why higher temperature increases evaporation rates and reaction rates: a larger fraction of particles has enough kinetic energy to escape a liquid surface or overcome an activation barrier.

Thermodynamic Processes and the First Law

The first law of thermodynamics is energy conservation applied to thermodynamic systems. Using the sign convention that $W$ is work done by the system,

$Δ U = Q - W$

where $Δ U$ is the change in internal energy and $Q$ is heat transferred into the system.

Common Processes

An isothermal process occurs at constant temperature. For an ideal gas, internal energy depends only on temperature, so the internal-energy change is zero during an ideal isothermal process.

An isochoric process occurs at constant volume. Because the boundary does not move, pressure-volume work is zero.

An isobaric process occurs at constant pressure. For expansion or compression at constant pressure, the magnitude of pressure-volume work is $W = p Δ V$ under the sign convention above.

An adiabatic process involves no heat transfer, so $Q = 0$ . A rapid compression can raise gas temperature because work is done on the gas.

On a pressure-volume diagram, the work done by a gas during a quasistatic expansion is the area under the process curve:

$W = \int p d V$

The Second Law, Entropy, and Heat Engines

The second law of thermodynamics gives a direction to spontaneous macroscopic processes. Heat flows spontaneously from a hotter body to a colder body, not the reverse, unless external work or another compensating change is involved.

Entropy is a thermodynamic state function. For a reversible transfer of heat at absolute temperature $T$ , the entropy change can be written $d S = δ Q_{r e v} / T$ . For an isolated system, total entropy does not decrease. At a statistical level, higher entropy is associated with macrostates compatible with larger numbers of microscopic arrangements.

Heat Engines and Carnot Efficiency

A heat engine absorbs energy from a hot reservoir, converts part of that energy into work, and rejects the remainder to a colder reservoir. No cyclic heat engine operating between two reservoirs can be more efficient than a reversible Carnot engine operating between the same temperatures.

For ideal reservoirs at $T_{H}$ and $T_{C}$ in kelvins, the maximum Carnot efficiency is:

$η_{C} = 1 - \frac{T_{C}}{T_{H}}$

Datei:Carnot cycle pV diagram.svg

The Carnot limit is not a claim that real engines reach this efficiency. Friction, finite temperature differences, turbulence, heat leaks, and other irreversible effects reduce practical efficiency.

Thermal Radiation

All objects with temperature above absolute zero emit electromagnetic radiation. A blackbody is an ideal absorber and emitter used as a reference model.

The Stefan-Boltzmann law for emitted thermal power is:

$P = ε σ A T^{4}$

where $ε$ is emissivity, $σ$ is the Stefan-Boltzmann constant, $A$ is surface area, and $T$ is thermodynamic temperature. Net radiative transfer to surroundings at temperature $T_{s}$ can be modeled as $P_{n e t} = ε σ A (T^{4} - T_{s}^{4})$ .

Wien's displacement law relates the wavelength of maximum spectral radiance to temperature:

$λ_{m a x} T = b$

As temperature rises, the peak shifts to shorter wavelengths and the total emitted power increases strongly.

Fehler beim Erstellen des Vorschaubildes:

Thermal imaging, infrared astronomy, climate science, industrial temperature measurement, and furnace design all use thermal-radiation concepts.

Worked Examples

Example: Heating Water

A 0.50 kg sample of water with specific heat capacity 4180 J kg⁻¹ K⁻¹ warms by 12 K. Using $Q = m c Δ T$ , the required energy is $Q = 0.50 \times 4180 \times 12 = 25080$ J, about 25 kJ. This ideal calculation ignores heat absorbed by the container and losses to the surroundings.

Example: Constant-Temperature Gas Expansion

An ideal gas expands isothermally from 2.0 L to 5.0 L. If its initial pressure is 250 kPa, Boyle's law gives $p_{1} V_{1} = p_{2} V_{2}$ , so $p_{2} = 250 \times 2.0 / 5.0 = 100$ kPa. The decrease in pressure follows from the larger volume available to the same number of particles at unchanged temperature.

Example: Carnot Limit

A heat engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. Its maximum theoretical efficiency is $η_{C} = 1 - 300 / 600 = 0.50$ , or 50 percent. A real engine working between the same reservoir temperatures must have a lower efficiency.

Interactive Tasks

Quiz: Test Your Knowledge

Which SI temperature unit should be used in the ideal gas law? (Kelvin) (!Celsius) (!Fahrenheit) (!Joule)

What best describes thermal equilibrium between two systems? (They have no net heat transfer between them) (!They contain the same total internal energy) (!They have the same mass) (!They contain the same number of particles)

Which equation models heating with no phase change? (Q equals mc delta T) (!Q equals mL) (!pV equals nR) (!W equals mg)

What happens ideally to temperature during a phase change at fixed pressure? (It remains approximately constant) (!It always doubles) (!It falls to absolute zero) (!It becomes independent of pressure forever)

What microscopic process produces gas pressure on a container wall? (Particle collisions with the wall) (!Gravitational attraction between all gas particles) (!Radiation escaping from the container) (!A permanent outward force stored in the gas)

For a fixed amount of ideal gas at constant temperature, what happens to pressure if volume doubles? (It halves) (!It doubles) (!It quadruples) (!It stays unchanged)

A gas receives 500 J of heat and does 200 J of work. What is its change in internal energy using delta U equals Q minus W? (300 J increase) (!700 J increase) (!300 J decrease) (!200 J increase)

What is true of an adiabatic process? (No heat is transferred) (!Temperature must stay constant) (!Pressure must stay constant) (!Volume must stay constant)

What is the Carnot efficiency for reservoirs at 600 K and 300 K? (50 percent) (!25 percent) (!75 percent) (!100 percent)

According to Wien's displacement law, how does the peak wavelength change as temperature rises? (It shifts to shorter wavelength) (!It shifts to longer wavelength) (!It stays fixed) (!It becomes zero at every finite temperature)

Memory Game

Thermal equilibrium	State with no net heat flow between systems in contact
Specific heat capacity	Energy required per unit mass for a unit temperature rise
Latent heat	Energy per unit mass transferred during a phase change
Ideal gas	Simplified particle model with negligible intermolecular forces except during collisions
Entropy	State function that tracks thermodynamic dispersal and multiplicity
Blackbody	Ideal reference object that absorbs and emits radiation perfectly

Drag and Drop

Match the correct terms.	Topic
Conduction	Energy transfer through microscopic interactions in matter
Convection	Energy transfer by bulk motion of a fluid
Radiation	Energy transfer by electromagnetic waves
Isothermal	Thermodynamic process at constant temperature
Adiabatic	Thermodynamic process with no heat transfer

...

Crossword Puzzle

Kelvin	Which thermodynamic temperature unit starts at absolute zero
Entropy	Which state function does not decrease for an isolated system
Conduction	Which heat-transfer mechanism acts through microscopic interactions in matter
Radiation	Which heat-transfer mechanism can cross a vacuum
Isothermal	What one-word adjective describes a constant-temperature process
Calorimetry	What technique measures heat transfer using temperature changes and known thermal properties

LearningApps

Cloze Text

Thermal physics connects microscopic particle behavior with macroscopic quantities such as

. Energy transferred because of a temperature difference is called

. For heating without phase change, the relation Q equals mc delta T uses the material property

. During a phase change, the energy per unit mass is described by

. An ideal gas is modeled by the equation

. The first law can be written delta U equals Q minus

. A process with no heat transfer is called

. For an isolated system, total

does not decrease. The maximum efficiency of a reversible engine between two reservoirs is the

. A hotter blackbody has a peak spectrum at a

.

Open-Ended Tasks

Easy

Temperature audit: Measure temperatures in several safe locations at school or home, record uncertainty, convert values from degrees Celsius to kelvins, and explain which differences are physically meaningful.
Simple calorimetry: Design a safe experiment using warm water and a known mass to estimate an energy transfer with Q equals mc delta T, then identify at least three sources of uncertainty.
Heating curve: Create and annotate a heating curve for a pure substance, showing where temperature rises and where phase changes occur, and explain the particle-level changes in each region.
Insulation comparison: Compare two everyday insulating materials with a controlled cooling test, graph temperature against time, and explain which heat-transfer mechanisms influence the result.

Standard

Gas law investigation: Use a simulation or laboratory apparatus to vary one gas state variable while controlling another, plot the data, and test a gas-law relationship quantitatively.
Cooling experiment: Record the cooling of a warm object or liquid over time, discuss why the cooling rate changes, and evaluate how room temperature and container geometry affect the data.
Brownian motion model: Produce a short video, animation, or physical model that explains how random molecular collisions can generate an irregular visible path without giving molecules a preferred direction.
Building heat-transfer survey: Inspect a classroom, workshop, or home for conduction, convection, and radiation pathways, document them with images or diagrams, and propose realistic energy-saving improvements.

Advanced

Heat engine case study: Research a real heat engine such as a steam turbine or internal-combustion engine, identify its hot and cold reservoirs, estimate a Carnot upper bound, and explain why real efficiency is lower.
Blackbody spectrum analysis: Use spectral data or a simulation to compare blackbody curves at different temperatures, test Wien's displacement relationship, and discuss a real application such as astronomy or thermal imaging.
Entropy and irreversibility: Analyze an irreversible process such as free expansion, mixing, frictional heating, or heat flow across a finite temperature difference, and explain the entropy change at both macroscopic and microscopic levels.
Statistical thermal model: Write a spreadsheet or computer program that generates a large set of random particle speeds or energy states, visualize the distribution, and explain how increasing temperature changes the statistical pattern.

Learning Assessment

Energy transfer analysis: Given a multi-stage heating problem that includes temperature change and a phase change, choose the correct equations, calculate the total energy, and justify each stage.
Gas-process reasoning: Interpret a pressure-volume graph containing isochoric, isobaric, isothermal, and adiabatic segments, then determine where work is done and explain the sign of the energy transfers.
Model evaluation: Compare the ideal-gas model with a real gas at high pressure or low temperature and explain which assumptions become less accurate and why.
Engine efficiency evaluation: Compare a stated real-engine efficiency with the Carnot limit for the same reservoir temperatures and judge whether the claim is physically possible.
Thermal design challenge: Propose a container or building component that minimizes unwanted heat transfer and defend the design using conduction, convection, and radiation.
Microscopic explanation: Explain how molecular collisions, speed distributions, and internal energy connect a measured temperature change to microscopic behavior.
Radiation transfer problem: Predict how changing surface area, emissivity, object temperature, and surroundings temperature affects net radiative power and support the prediction with the Stefan-Boltzmann relationship.

Evidence of Learning

Evidence of learning should show more than formula recall. Strong evidence includes accurate use of thermodynamic vocabulary; correct selection and rearrangement of equations; unit-aware calculations; interpretation of heating curves, phase diagrams, pressure-volume graphs, and molecular-speed distributions; clear particle-level explanations; experimental data with uncertainty analysis; well-designed graphs; reasoned evaluation of model assumptions; safe and repeatable laboratory procedures; and transfer of thermal-physics ideas to engines, buildings, climate systems, manufacturing, refrigeration, astronomy, and everyday technologies.

Products may include a laboratory report, annotated diagram, calculation portfolio, simulation, spreadsheet model, thermal-design proposal, explanatory video, interview summary, or research poster. Your work should make assumptions explicit and distinguish measured data, calculated values, model predictions, and qualitative inference.

OERs on the Topic

Linked Learning Areas

Thermal Physics

Thermal physics connects strongly with physics, chemistry, engineering, environmental science, astronomy, meteorology, materials science, and technical fields involving energy systems, refrigeration, heating, ventilation, process control, engines, and thermal measurement.