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Theme B — The Particulate Nature of Matter

B.1.8 Specific Heat Capacity — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 10 of 53 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

B.1.8 Specific Heat Capacity — IB PHYSICS SL notes: Use Q = mcΔT to calculate thermal energy transfers and describe how to measure specific heat capacity.Specific heat capacity c = the amount of energy required to change the temperature of 1 kg of a substance by 1 K (or 1 °C).The…

  • What the symbols mean
  • Rearranged
  • Heat capacity of an object
  • Temperature changes
  • Energy sharing
  • Many ways to store energy

Section 1 of 9Definition

1Specific heat capacity c
Specific heat capacity c the amount of energy required to change the temperature of 1 kg of a substance by 1 K (or 1 °C).
  • The unit is J kg−1 K−1.
2Equation
  • Q = mcΔT.
    What the symbols mean: E, Q or q = energy transferred (J) · m = mass · c = specific heat capacity (J kg−1 °C−1; water 4.18 J g−1 °C−1) · ΔT or Δθ = temperature change (°C or K)
    • (kg; g in chemistry calorimetry)
  • Q is the thermal energy transferred in J.
  • m is the mass in kg.
  • ΔT is the temperature change in K or °C.
3Cooling
  • ΔT and Q are negative, meaning energy is released.
4Rearranged
  • Rearranged c = Q/(mΔT).
5Heat capacity of an object
  • C = mc in J K−1, so Q = CΔT.
6Factors
  • Factors the energy needed depends on the temperature change, the mass and the substance.

Section 2 of 9Typical values

Substancec / J kg−1 K−1
Water4200
Ice2200
Aluminium900
Copper390
Gold130
Large c
  • Large c a lot of energy is needed to change the temperature, so the substance warms and cools slowly.
Water
  • Water its high value makes it a good coolant and moderates coastal climates.
Metals
  • Metals they heat up and cool down much faster than water.
Temperature changes
  • ΔT can be in °C without converting to kelvin.

Section 3 of 9Why substances differ

Why substances differ
Energy sharing
  • Energy sharing energy is shared between random kinetic energy,
    • which raises the temperature,
    • and potential energy and other modes such as rotation and vibration.
Many ways to store energy
  • Many ways to store energy materials with these have higher c.
Strong bonds
  • Strong bonds hydrogen bonds in water raise c per kilogram.
Light particles
  • Light particles more particles per kilogram must each gain energy.

Section 4 of 9Electrical method

1
Wrap a metal block with holes for a heater and a thermometer in insulation.
2
Record the initial temperature and run the heater of known power P = VI for a time t.
3
Record the final temperature.
4
Calculate c = VIt/(mΔT).
Better contact
  • Better contact add a little oil in the thermometer hole.
Liquid
  • Liquid stir it.
Graph
  • Graph plot temperature against time; the gradient is P/(mc), so c = P/(m × gradient).
Advantage
  • Advantage the gradient averages random errors and ignores a fixed offset in the start time.

Section 5 of 9Method of mixtures

1
Heat a metal sample in boiling water to about 100 °C.
2
Transfer it quickly to a known mass of cool water in an insulated calorimeter.
3
Measure the final temperature.
4
Equate energy lost by the metal to energy gained by water and calorimeter, and solve for c.
  • Errors
    • energy lost during the transfer, water carried over with the metal and energy absorbed by the calorimeter.

Section 6 of 9Errors and improvements

Heat loss
  • Heat loss it makes ΔT too small, so c appears too high.
Graph curving over
  • Graph curving over losses grow as the sample gets hotter, so use the initial gradient.
Reducing loss
  • Reducing loss lagging, a lid and starting a few degrees below room temperature so that the average temperature is near room temperature.
Random errors
  • Random errors reading the thermometer and timing.
Reporting
  • Reporting give a sensible number of significant figures and the percentage difference from the accepted value.
Constant power
  • Constant power the temperature rises linearly with gradient P/(mc) until a change of state.

Section 7 of 9More from the specification

1
Calorimetric thermal storage in solids
  • Calorimetric thermal storage in solids measuring energy absorbed per kelvin across dense mineral solids determines specific heat capacity on Earth.
2
Thermal Energy Transfer Mechanisms
  • Thermal energy transfers through matter via conduction in a solid and convection in fluids (density differences),
    • (molecular vibrations and free electron diffusion)
  • whereas thermal radiation transfers energy across vacuums via electromagnetic waves emitted from an object's surface.
3
Specific Latent Heat and Phase Changes
  • During a phase change, absorbed thermal energy increases the potential energy of molecules and breaks intermolecular bonds at constant temperature, governed by Q = m·L.
    • (such as melting of a solid or vaporisation of a liquid)
4
Stefan-Boltzmann Law and Stellar Luminosity
  • The total radiative power or luminosity L emitted from a celestial body's surface of area A and absolute temperature T is given by the Stefan-Boltzmann law L = σ·A·T⁴, transferring energy purely via radiation.
5
Fusion
  • Joining of light nuclei into a heavier one.
6
Intensity
  • Power per unit area perpendicular to the wave direction.
7
Apparent brightness
  • The power received per unit area at the observer
8
Thermal equilibrium
  • Constant temperature because energy is absorbed and lost at equal rates
9
Phase change
  • Change of matter from one state to another
10
Thermal conductivity
  • Material constant relating the rate of conduction to the temperature gradient and area
11
Internal energy
  • Total kinetic and potential energy of the particles in a system
12
Surface temperature
  • Effective temperature of the star's radiating surface.
13
Radiation
  • Transfer by electromagnetic waves, requiring no medium
14
Convection
  • Transfer of thermal energy by the movement of a heated fluid
15
Conduction
  • Transfer of thermal energy by lattice vibrations and free electrons
16
Molecule
  • Tiny particle of the fluid, too small to be seen.
17
Luminosity
  • The total power of radiation emitted by a star.
18
Density
  • Mass per unit volume.
19
Wavelength
  • Distance between a point on one wave and the same point on the next wave
20
Solid
  • State with a fixed shape and a fixed volume.

Section 8 of 9Key terms

TermMeaning
Specific heat capacityEnergy needed to raise the temperature of 1 kg of a substance by 1 K
Heat capacityEnergy needed to raise the temperature of an object by 1 K
CalorimeterInsulated container used to measure energy changes
Method of mixturesTechnique using energy lost by a hot sample equal to energy gained by cooler water
LaggingInsulation used to reduce heat losses
Thermal contactArrangement allowing energy to pass between two bodies

Section 9 of 9Exam technique

1
Using Q = mcΔT during a change of state — use Q = mL there.
2
Forgetting the sign of ΔT when cooling — Q is negative.
3
Converting ΔT to kelvin by adding 273 — only temperature differences are needed, so no conversion.
4
Using grams with J kg−1 K−1 — convert to kilograms.
5
Saying heat loss makes c appear too low — it makes it too high.

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