Unit 11 - Grade 11-12 Physics

Thermal Physics and Gas Laws

Learn temperature, heat, internal energy, specific heat, phase changes, heat transfer, kinetic molecular theory, ideal gases, gas laws, thermodynamic processes, and real-world energy applications.

Lesson roadmap

What Students Should Master in This Unit

Thermal physics connects microscopic particle motion to macroscopic measurements such as temperature, pressure, volume, heat, and energy. Students learn how energy is stored, transferred, conserved, and modeled in gases and materials.

Explain heat and temperature

Distinguish thermal energy, internal energy, heat transfer, and temperature scales.

Solve thermal energy problems

Use specific heat, latent heat, calorimetry, expansion, and heat-transfer equations.

Analyze gases and thermodynamics

Apply kinetic molecular theory, gas laws, ideal gas law, PV diagrams, and the first law.

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Thermal Basics Temperature Scales Heat and Internal Energy Thermal Expansion Specific Heat and Calorimetry Phase Changes Heat Transfer Kinetic Molecular Theory Gas Laws Ideal Gas Law Thermodynamics Simulation Labs Lab Skills Worked Examples Practice Problems
Energy at the particle level

1. Thermal Physics Basics

Thermal physics studies how matter behaves when energy is transferred as heat. It explains temperature, phase changes, engines, refrigerators, weather, cooking, materials, and gas behavior.

Thermal physics at the particle level Thermal energy begins with particle motion cooler: lower average KE hotter: higher average KE heat transfer Q
Temperature tracks average particle kinetic energy, while heat is energy transferred because of a temperature difference.
Quantity Meaning Common Unit
Temperature TAverage kinetic energy per particlekelvin, K
Heat QEnergy transferred because of temperature differencejoule, J
Internal energy UTotal microscopic kinetic and potential energyjoule, J
Specific heat cEnergy needed to raise 1 kg by 1 K or 1°CJ/(kg·°C)
Latent heat LEnergy per kg for a phase changeJ/kg
Pressure PForce per area from particle collisionspascal, Pa
Core idea: Heat is energy in transit. Temperature is a measurement. Internal energy is energy stored inside the system.
Celsius, kelvin, and Fahrenheit

2. Temperature Scales

Temperature measures how hot or cold something is. In physics formulas involving gases and thermal energy, kelvin is usually required.

Temperature scales used in thermal physics Gas laws require absolute temperature in kelvin 373 K = 100°C 273 K = 0°C 0 K = -273°C T(K) = T(°C) + 273.15
Kelvin starts at absolute zero, so gas-law ratios and PV = nRT must use kelvin instead of Celsius.
Celsius to kelvin T(K) = T(°C) + 273.15 Use kelvin for gas laws.
Kelvin to Celsius T(°C) = T(K) - 273.15 Celsius is common in lab measurements.
Celsius to Fahrenheit T(°F) = 9/5T(°C) + 32 Useful for everyday comparisons.
Temperature change ΔT(K) = ΔT(°C) A change of 1 K equals a change of 1°C.
Absolute zero 0 K = -273.15°C Lowest possible temperature on the kelvin scale.
Room temperature 20°C to 25°C = about 293 K to 298 K Useful estimate for gas problems.
Common mistake: Never use Celsius directly in PV = nRT or gas law ratios unless the problem only uses temperature change where ΔT is allowed.
Energy transfer versus energy stored

3. Heat, Temperature, and Internal Energy

Heat and temperature are related, but they are not the same. Heat is energy transferred from hotter objects to colder objects. Temperature describes average particle kinetic energy.

Heat, temperature, and internal energy Heat flows because of temperature difference hot object higher T cold object lower T Q Thermal equilibrium: Thot = Tcold
Heat is energy crossing a boundary; internal energy is the microscopic energy stored in the particles of the system.
Heat transfer direction hot object -> cold object Spontaneous heat flow goes from higher temperature to lower temperature.
Thermal equilibrium Thot = Tcold No net heat transfer once temperatures match.
Internal energy of ideal monatomic gas U = 3/2 nRT Advanced but useful for thermodynamics problems.

Important Distinctions

  • A large cold object can have more internal energy than a small hot object because it has more particles.
  • Temperature depends on average particle kinetic energy, not total energy.
  • Heat only describes energy transfer while it is crossing a system boundary.
Matter changes size with temperature

4. Thermal Expansion

Most materials expand when heated and contract when cooled because particles move more vigorously and average separation increases.

Thermal expansion Materials usually expand when temperature rises cooler rod heat ΔL = αL0ΔT shorter longer
Thermal expansion is why bridges, tracks, pipes, and glassware must allow room for temperature changes.
Linear expansion ΔL = αL0ΔT Length change for rods, rails, wires, and beams.
Area expansion ΔA = 2αA0ΔT Approximation for isotropic solids.
Volume expansion ΔV = βV0ΔT For liquids and solids; often β is about 3α for solids.

Applications

  • Expansion gaps are left in bridges and railroad tracks.
  • Thermostats can use bimetallic strips that bend when heated.
  • Glassware can crack if temperature changes too quickly.
Changing temperature without changing phase

5. Specific Heat and Calorimetry

Specific heat tells how much energy is needed to change an object's temperature. Water has a high specific heat, so it resists temperature changes more than many materials.

Specific heat and calorimetry Calorimetry tracks heat lost and heat gained hot metal Q = mcΔT Qlost + Qgained = 0 for an insulated system
In calorimetry, heat lost by a warmer material is gained by a cooler material, after accounting for the container when needed.
Heat for temperature change Q = mcΔT Use when phase does not change.
Calorimetry principle Qlost + Qgained = 0 For an insulated system.
Water specific heat cwater = 4186 J/(kg·°C) Often rounded to 4200 J/(kg·°C).

Common Specific Heats

Material Approximate Specific Heat Meaning
Water4186 J/(kg·°C)Large energy needed for temperature change.
Ice2100 J/(kg·°C)Less than liquid water.
Steam2010 J/(kg·°C)Water vapor heat capacity.
Aluminum900 J/(kg·°C)Warms faster than water for same mass and heat.
Copper385 J/(kg·°C)Good conductor with low specific heat.
Iron450 J/(kg·°C)Common metal in lab examples.
Changing state at constant temperature

6. Phase Changes and Latent Heat

During a phase change, added or removed energy changes particle arrangement instead of changing temperature. That is why temperature stays constant during melting or boiling for a pure substance at constant pressure.

Heating curve and latent heat During a phase change, temperature stays constant T heat added melting plateau boiling plateau Q = mcΔT on slopes, Q = mL on plateaus
Use Q = mcΔT when temperature changes, and use Q = mL when the substance changes phase.
Latent heat Q = mL Use during melting, freezing, boiling, or condensing.
Fusion of water Lf = 3.34 × 105 J/kg Energy to melt ice at 0°C.
Vaporization of water Lv = 2.26 × 106 J/kg Energy to boil water at 100°C.

Heating Curve Steps for Water

  1. Warm ice below 0°C using Q = mcΔT.
  2. Melt ice at 0°C using Q = mLf.
  3. Warm liquid water from 0°C to 100°C using Q = mcΔT.
  4. Vaporize water at 100°C using Q = mLv.
  5. Warm steam above 100°C using Q = mcΔT.
Common mistake: Do not use Q = mcΔT during a phase change. Use Q = mL because temperature is constant during the phase transition.
How thermal energy moves

7. Heat Transfer: Conduction, Convection, and Radiation

Thermal energy can move through direct contact, fluid motion, or electromagnetic radiation. Many real systems use all three at once.

Three heat transfer mechanisms Heat moves by conduction, convection, and radiation conduction convection radiation
Conduction needs contact, convection needs moving fluid, and radiation can transfer energy through empty space.
Conduction rate Q/t = kAΔT/L k is thermal conductivity, L is thickness.
Radiation power P = eσAT4 Stefan-Boltzmann law for thermal radiation.
Net radiation Pnet = eσA(T4 - Tenv4) Temperatures must be in kelvin.
Mechanism How It Works Example
ConductionEnergy transfer by particle collisions through matterA metal spoon heating in soup.
ConvectionEnergy transfer by bulk fluid motionWarm air rising above a heater.
RadiationEnergy transfer by electromagnetic wavesSunlight warming Earth.
Gas behavior from particle motion

8. Kinetic Molecular Theory

Kinetic molecular theory explains gas pressure and temperature using moving particles. Gas particles collide with container walls, producing pressure.

Kinetic molecular theory Gas pressure comes from particle collisions wall collision higher T faster particles, more energetic collisions KEavg = 3/2 kBT
As temperature rises, particles move faster, collide with walls more strongly, and can increase gas pressure if volume is fixed.
Average translational kinetic energy KEavg = 3/2 kBT Temperature must be in kelvin.
Root-mean-square speed vrms = √(3RT/M) M is molar mass in kg/mol.
Pressure from particles higher T -> faster particles -> higher pressure If volume and amount of gas are fixed.

Ideal Gas Assumptions

  • Gas particles are very small compared with the space between them.
  • Particles move randomly and constantly.
  • Collisions are elastic.
  • Intermolecular forces are ignored except during collisions.
Pressure, volume, temperature, and amount

9. Gas Laws

Gas laws describe how pressure, volume, temperature, and moles are related when some variables are held constant.

Gas law variables Gas laws compare P, V, T, and n P, V, T, n hold some constant solve for the change Boyle, Charles, Gay-Lussac, Avogadro
Gas-law problems are usually about identifying which variables change and which variables are held constant.
Boyle's law P1V1 = P2V2 Temperature and amount constant. P and V are inverse.
Charles's law V1/T1 = V2/T2 Pressure and amount constant. Use kelvin.
Gay-Lussac's law P1/T1 = P2/T2 Volume and amount constant. Use kelvin.
Avogadro's law V1/n1 = V2/n2 Pressure and temperature constant.
Combined gas law P1V1/T1 = P2V2/T2 Use when n is constant.
Standard temperature and pressure STP = 273.15 K and 1 atm Common reference condition.
One equation for ideal gases

10. Ideal Gas Law

The ideal gas law combines pressure, volume, amount of gas, and absolute temperature into one equation.

Ideal gas law map PV = nRT connects the full gas state PV = nRT pressure P volume V moles n kelvin T
PV = nRT works only when units match the gas constant being used, so kelvin and SI units matter.
Ideal gas law PV = nRT P in Pa, V in m3, T in K, n in mol.
Gas constant R = 8.314 J/(mol·K) Use with SI units.
Particle version PV = NkBT N is number of particles, kB is Boltzmann's constant.

Unit Checklist for PV = nRT

  • Pressure must be in pascals if R = 8.314 J/(mol·K).
  • Volume must be in cubic meters.
  • Temperature must be in kelvin.
  • Moles can be found from n = mass / molar mass.
Energy conservation in thermal systems

11. Thermodynamics, Work, and PV Diagrams

Thermodynamics studies heat, work, and changes in internal energy. A gas can gain energy by heat input or by work done on it, and it can lose energy by doing work on the surroundings.

Thermodynamics and PV work Work by a gas is the area under a PV curve P V area = W ΔU = Q - W heat added changes internal energy and/or becomes work
PV diagrams turn gas expansion or compression into geometry: area under the curve represents work.
First law of thermodynamics ΔU = Q - W W is work done by the system.
Work by gas at constant pressure W = PΔV Positive when gas expands.
Work from a PV graph W = area under P-V curve Area has units Pa·m3 = J.

Common Thermodynamic Processes

Process Constant Quantity Key Idea
IsothermalTemperatureΔU = 0 for an ideal gas.
IsobaricPressureWork can be found with W = PΔV.
IsochoricVolumeNo volume change, so W = 0.
AdiabaticNo heat transferQ = 0, so ΔU = -W.

Heat Engines and Efficiency

Efficiency e = Wout / Qin Useful work divided by heat input.
Engine energy balance Wout = Qin - Qout Heat rejected cannot be zero for real engines.
Carnot efficiency emax = 1 - Tcold/Thot Temperatures must be in kelvin.
Simulation labs

12. Simulation Labs for This Unit

These official PhET simulations help students visualize gas behavior, particle motion, phase changes, energy transfer, and thermal radiation.

Thermal simulation lab workflow Use simulations to test one thermal variable at a time Change T, V, heat, mass Measure P, phase, energy Explain use particles and formulas A strong simulation lab connects particle motion to the equation trend.
Simulations are most useful when students predict a trend, change one variable, collect evidence, and explain the result.
Gas Properties

Explore pressure, volume, temperature, particle motion, collisions, and the ideal gas relationship.

Lab idea: hold volume constant, increase temperature, and track how pressure changes.
Open Simulation
Gases Intro

Use a focused gas-law environment to connect pressure, volume, temperature, and particle number.

Lab idea: compare Boyle's law and Gay-Lussac's law by holding different variables constant.
Open Simulation
States of Matter

Observe particle motion in solids, liquids, and gases as temperature changes and phase transitions occur.

Lab idea: heat a substance and identify when energy changes temperature versus phase.
Open Simulation
Energy Forms and Changes

Track energy transfer between systems and connect heating, cooling, and energy conservation.

Lab idea: compare how different materials warm up under the same energy input.
Open Simulation
Blackbody Spectrum

Investigate how thermal radiation changes with temperature and how hotter objects emit more intense radiation.

Lab idea: increase temperature and observe the shift in peak wavelength and intensity.
Open Simulation
Investigation skills

13. Thermal Physics and Gas Laws Lab Skills

Thermal labs require careful control of variables because heat can escape into the container, air, thermometer, and surroundings.

Thermal physics lab measurements Thermal labs need careful units and heat-loss awareness temperature volume change pressure record mass, temperature, time, pressure, volume, and power with units
Thermal lab quality improves when students track units, insulation, heat loss, and whether temperature is Celsius or kelvin.

Common Labs

  • Specific heat calorimetry lab.
  • Latent heat of fusion lab using ice and water.
  • Cooling curve or heating curve investigation.
  • Thermal expansion demonstration.
  • Boyle's law pressure-volume lab.
  • Charles's law volume-temperature lab.
  • Gas pressure-temperature lab at constant volume.
  • Heat transfer comparison lab for conduction, convection, and radiation.

Useful Measurements

  • Mass in kilograms.
  • Temperature in Celsius for lab readings, then kelvin for gas laws.
  • Pressure in pascals or kilopascals.
  • Volume in cubic meters or liters converted correctly.
  • Time interval for heating or cooling rate.
  • Power input in watts for electrical heating labs.
Lab warning: A calorimeter is not perfectly insulated. Good lab reports discuss heat loss, thermometer delay, incomplete mixing, and uncertainty in mass and temperature.
Worked examples

14. Worked Examples

Example 1: Convert Celsius to kelvin

Convert 27°C to kelvin.

T = 27 + 273.15 = 300.15 K, about 300 K.

Example 2: Heat to warm water

How much heat warms 0.50 kg of water from 20°C to 80°C?

Q = mcΔT = (0.50)(4186)(60) = 1.26 × 105 J.

Example 3: Specific heat

A 2.0 kg metal gains 9000 J and warms by 10°C. Find specific heat.

c = Q/(mΔT) = 9000/[(2.0)(10)] = 450 J/(kg·°C).

Example 4: Melting ice

How much energy melts 0.20 kg of ice at 0°C?

Q = mLf = (0.20)(3.34 × 105) = 6.68 × 104 J.

Example 5: Thermal expansion

A 10 m steel rail with α = 1.2 × 10-5/°C warms by 40°C. Find length change.

ΔL = αL0ΔT = (1.2 × 10-5)(10)(40) = 0.0048 m.

Example 6: Boyle's law

A gas at 100 kPa has volume 2.0 L. Pressure rises to 250 kPa at constant temperature. Find final volume.

P1V1 = P2V2.

V2 = (100)(2.0)/250 = 0.80 L.

Example 7: Charles's law

A gas volume is 3.0 L at 300 K. If temperature rises to 450 K at constant pressure, find final volume.

V1/T1 = V2/T2.

V2 = (3.0)(450/300) = 4.5 L.

Example 8: Ideal gas law

Find pressure of 2.0 mol of gas in 0.050 m3 at 300 K.

P = nRT/V = (2.0)(8.314)(300)/0.050 = 9.98 × 104 Pa.

Example 9: First law

A gas absorbs 500 J of heat and does 200 J of work. Find change in internal energy.

ΔU = Q - W = 500 - 200 = 300 J.

Example 10: Heat engine efficiency

An engine takes in 1000 J of heat and outputs 250 J of work. Find efficiency.

e = Wout/Qin = 250/1000 = 0.25 = 25%.

Independent practice

15. Practice Problems

Try each problem first. Then open the answer check and compare formulas, unit conversions, signs, and reasoning.

1. Convert 45°C to kelvin.

Answer

T = 45 + 273.15 = 318.15 K.

2. Convert 250 K to Celsius.

Answer

T(°C) = 250 - 273.15 = -23.15°C.

3. How much heat warms 1.0 kg of water by 25°C?

Answer

Q = mcΔT = (1.0)(4186)(25) = 1.05 × 105 J.

4. A 0.40 kg metal absorbs 3600 J and warms by 20°C. Find c.

Answer

c = Q/(mΔT) = 3600/[(0.40)(20)] = 450 J/(kg·°C).

5. How much energy melts 0.050 kg of ice at 0°C?

Answer

Q = mLf = (0.050)(3.34 × 105) = 1.67 × 104 J.

6. How much energy boils 0.10 kg of water already at 100°C?

Answer

Q = mLv = (0.10)(2.26 × 106) = 2.26 × 105 J.

7. A 5.0 m aluminum rod with α = 2.4 × 10-5/°C warms by 30°C. Find ΔL.

Answer

ΔL = αL0ΔT = (2.4 × 10-5)(5.0)(30) = 0.0036 m.

8. Heat flows through a wall by conduction. What happens to heat-transfer rate if wall thickness doubles?

Answer

Rate is cut in half because Q/t = kAΔT/L.

9. Name the three heat transfer mechanisms.

Answer

Conduction, convection, and radiation.

10. A gas has P1 = 120 kPa and V1 = 4.0 L. If volume decreases to 2.0 L at constant temperature, find P2.

Answer

P2 = P1V1/V2 = (120)(4.0)/2.0 = 240 kPa.

11. A gas volume is 2.0 L at 300 K. It is heated to 600 K at constant pressure. Find final volume.

Answer

V2 = V1T2/T1 = (2.0)(600/300) = 4.0 L.

12. A gas pressure is 100 kPa at 300 K. Temperature increases to 450 K at constant volume. Find pressure.

Answer

P2 = P1T2/T1 = (100)(450/300) = 150 kPa.

13. A gas has P1 = 100 kPa, V1 = 3.0 L, T1 = 300 K. If P2 = 150 kPa and T2 = 450 K, find V2.

Answer

P1V1/T1 = P2V2/T2.

V2 = (P1V1T2)/(T1P2) = (100)(3.0)(450)/[(300)(150)] = 3.0 L.

14. Find volume of 1.0 mol ideal gas at 1.01 × 105 Pa and 273 K.

Answer

V = nRT/P = (1.0)(8.314)(273)/(1.01 × 105) = 0.0225 m3, about 22.5 L.

15. Find moles of gas if P = 2.0 × 105 Pa, V = 0.030 m3, and T = 300 K.

Answer

n = PV/RT = (2.0 × 105)(0.030)/[(8.314)(300)] = 2.4 mol.

16. A gas absorbs 800 J of heat and does 500 J of work. Find ΔU.

Answer

ΔU = Q - W = 800 - 500 = 300 J.

17. A gas at constant pressure 2.0 × 105 Pa expands from 0.010 m3 to 0.030 m3. Find work done by the gas.

Answer

W = PΔV = (2.0 × 105)(0.020) = 4000 J.

18. An engine takes in 2000 J and rejects 1400 J. Find useful work and efficiency.

Answer

W = Qin - Qout = 2000 - 1400 = 600 J.

e = W/Qin = 600/2000 = 0.30 = 30%.

19. A Carnot engine operates between 600 K and 300 K. Find maximum efficiency.

Answer

emax = 1 - Tcold/Thot = 1 - 300/600 = 0.50 = 50%.

20. In the Gas Properties simulation, if volume and particle number stay constant, what happens to pressure when temperature increases?

Answer

Pressure increases because faster particles collide harder and more often with the container walls.

Final review

16. What to Know Before Moving On

  • Heat is energy transferred because of temperature difference.
  • Temperature in gas laws must be measured in kelvin.
  • For temperature change without phase change, use Q = mcΔT.
  • For phase change at constant temperature, use Q = mL.
  • Heat transfers by conduction, convection, and radiation.
  • Gas temperature is proportional to average particle kinetic energy.
  • Boyle's law relates pressure and volume at constant temperature.
  • Charles's law and Gay-Lussac's law require kelvin temperatures.
  • The ideal gas law is PV = nRT.
  • The first law of thermodynamics is ΔU = Q - W when W is work done by the system.
  • Work done by a gas is the area under a P-V graph.
  • No real heat engine can convert all heat input into useful work.
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