Temperature & heat transfer

Learning goals

What students should be able to explain, calculate and investigate after completing Temperature and Heat Transfer.

Goals marked Higher Level are required only for Higher Level students; the remaining goals are for all students.

• Define temperature and distinguish it from heat energy.
• Convert between the Celsius and Kelvin temperature scales.
• Use Q = mcΔθ to calculate the heat energy needed to change temperature.
• Higher Level: Use Q = mL to calculate the heat energy needed to change state, distinguishing fusion from vaporisation.
• Describe conduction, convection and radiation using a particle model.
• Use the U-value to calculate the rate of heat loss through a material.
• Describe an experiment to determine specific heat capacity.
• Higher Level: Determine specific latent heat from primary data for fusion of ice or vaporisation of steam.

Key definitions

Precise terms, symbols and SI units used in Temperature and Heat Transfer.

Temperature and Temperature Scales

Temperature and heat are often confused.

Temperature tells you how hot or cold something is (related to the average kinetic energy of its particles); heat energy tells you how much energy is transferred. Two objects at the same temperature can require very different amounts of heat energy to reach that temperature, depending on their mass and specific heat capacity. The Celsius scale sets 0 °C at the freezing point of water and 100 °C at its boiling point (at standard pressure). The Kelvin scale starts at absolute zero — the lowest temperature theoretically possible, at which particles have the minimum possible kinetic energy (it is more accurate to describe absolute zero this way than to say there is 'no heat energy' at that point, since internal energy and the definition of 'heat' are distinct ideas). To convert: T(K) = θ(°C) + 273.15.

Thermometric Properties and Choosing a Thermometer

A thermometric property is a measurable physical property that changes predictably with temperature.

Examples include the volume of a liquid, electrical resistance, thermocouple emf and gas pressure at constant volume. A useful property changes consistently, is sensitive enough for the required range, responds quickly, is repeatable and can be calibrated against fixed reference temperatures.

• Primary data: place two temperature sensors together in warming water, record their readings at regular intervals and compare response time, range, sensitivity and repeatability.
• Secondary data: compare calibration graphs for possible thermometric properties. Look for a predictable relationship, adequate range and a large enough change per degree.
• A material is not “best” in every situation: suitability depends on the temperature range, required precision, response time, robustness and method of reading.

Heat Energy and Temperature Change

The energy needed to change an object's temperature depends on its mass, its specific heat capacity, and the size of the temperature change: Q = mcΔθ.

Different substances have different specific heat capacities — water has an unusually high specific heat capacity, which is why it heats up and cools down more slowly than most other common materials, and why it is used in heating systems and for climate moderation near large bodies of water.

Latent Heat and Change of State

When a substance changes state (melts, boils, freezes, or condenses) at a constant temperature, the energy supplied or released does not change its temperature.

This is why a heating curve shows flat plateaus at the melting point and boiling point, even though heat is still being supplied at a constant rate throughout.

Conduction, Convection and Radiation

Conduction transfers internal energy through a material without bulk movement of the material. In metals, mobile electrons make an important contribution.

Conduction transfers internal energy through collisions and lattice vibrations without bulk movement of matter; free electrons make metals especially effective conductors. Convection occurs only in fluids: heating causes expansion, lowers density and produces an upward buoyant force, while cooler denser fluid sinks. Thermal radiation is electromagnetic radiation and therefore needs no medium. A temperature difference sets the net direction of energy transfer.

U-Values and Heat Loss

The U-value of a material or building element (such as a wall, roof, or window) measures how quickly heat energy passes through it for a given temperature difference across it.

The rate of heat loss through a material is given by (rate of heat loss) = U × A × Δθ, where A is the area and Δθ is the temperature difference between the two sides. U-values are central to comparing insulation options and improving the energy efficiency of buildings.

Heat Pumps

A heat pump uses a circulating refrigerant and a compressor to transfer thermal energy from a colder outdoor reservoir to a warmer building.

The refrigerant is chosen so that it can boil at a low temperature in the evaporator and condense at a higher temperature in the condenser. The compressor supplies the work needed to move energy against its natural direction of transfer—from colder surroundings to a warmer interior. Energy is conserved: the thermal energy delivered indoors equals the thermal energy absorbed outdoors plus the electrical work supplied.

• In the evaporator, cold low-pressure refrigerant absorbs thermal energy from the surroundings and evaporates.
• The electrically driven compressor does work on the vapour, increasing its pressure and temperature.
• In the condenser, hot high-pressure refrigerant releases thermal energy to the building and condenses.
• The expansion valve lowers the refrigerant pressure and temperature before it returns to the evaporator.

Course scope: The new specification requires the concept of a heat pump and the concept of efficiency. It does not explicitly name coefficient of performance (COP) or include its formula in the equation list, so COP is presented here as a useful extension and real-life application rather than a formula that must be learned.

• COP_heating is the heating coefficient of performance: thermal energy delivered to the warm region per unit of work supplied.
• COP_cooling is the cooling coefficient of performance: thermal energy removed from the cold region per unit of work supplied.
• Q_hot is the thermal energy delivered to the warm region, such as the building.
• Q_cold is the thermal energy absorbed from the cold region, such as the outdoor surroundings.
• W is the external work supplied to the heat pump, normally by the electrically driven compressor.
• Q_hot, Q_cold and W must use the same energy unit. COP has no unit.

Diagrams and formulae

Key diagrams and equations for reviewing Temperature and Heat Transfer.

• Heating curve for ice → water → steam: the sloped sections show temperature rising as heat is absorbed (Q = mcΔθ); the flat plateaus show heat being absorbed with no temperature change while the substance changes state (Q = mL).
• The three modes of heat transfer: conduction (particle vibration in solids), convection (bulk fluid movement), and radiation (electromagnetic waves, no medium needed — dull/black surfaces absorb and emit better than shiny surfaces).
• U-value: the rate of heat loss through a material of area A depends on the U-value and the temperature difference Δθ across it.

Heating curve for ice → water → steam: the sloped sections show temperature rising as heat is absorbed (Q = mcΔθ); the flat plateaus show heat being absorbed with no temperature change while the substance changes state (Q = mL).

The three modes of heat transfer: conduction (particle vibration in solids), convection (bulk fluid movement), and radiation (electromagnetic waves, no medium needed — dull/black surfaces absorb and emit better than shiny surfaces).

U-value: the rate of heat loss through a material of area A depends on the U-value and the temperature difference Δθ across it.

• Key relationships
• Temperature conversion: T(K) = θ(°C) + 273.15 Q = mcΔθ Q = mL Rate of heat loss = U A Δθ (U-value;
• A = area, Δθ = temperature difference)

Worked Example

A step-by-step calculation applying the central relationships in Temperature and Heat Transfer.

Calculate the heat energy needed to raise the temperature of 2 kg of water from 20 °C to 80 °C. (Specific heat capacity of water, c = 4200 J kg⁻¹ K⁻¹.)

• Δθ = 80 − 20 = 60 °C (a change of 60 °C is the same size as a change of 60 K)
• Q = mcΔθ = 2 × 4200 × 60 = 504 000 J = 5.04 × 10⁵ J

Practical / Investigation

Experimental planning, measurement and evaluation for Temperature and Heat Transfer.

Experiment: Measuring the specific heat capacity of water (or a solid)

• Apparatus: immersion heater, joulemeter (or ammeter, voltmeter and stopwatch), calorimeter/insulated container, thermometer, balance.
• Method: measure the mass of water (or solid); record the initial temperature; supply a measured amount of electrical energy (using P = VI and t, or a joulemeter) while stirring gently; record the final temperature.
• Calculation: Q (electrical energy supplied) = mcΔθ, so c = Q/(mΔθ).
• Sources of error: heat lost to the surroundings and to the container itself (not all supplied energy raises the water's temperature); the thermometer's own heat capacity affects the result slightly.
• Improvement: use an insulated container (calorimeter) to reduce heat loss; stir continuously for even heating; take a cooling correction if heat loss is significant.

Higher Level: Measuring the specific latent heat of fusion of ice

• Method: add measured, dried ice (patted dry so no surface water is included — otherwise the added mass would wrongly include water that has already melted) to a measured mass of water in an insulated container at a temperature above 0 °C; record the temperature drop as the ice melts and mixes in.
• Calculation: heat lost by the water and container = heat gained melting the ice + heat gained warming the melted ice to the final temperature. Use this to find L for ice.
• Sources of error: ice not fully dried before adding (adds extra water mass); heat exchange with the surroundings.

Higher Level: Measuring the specific latent heat of vaporisation of water

• Method: pass steam from boiling water, through a steam trap (which removes water droplets carried along with the steam, so that only dry steam condenses into the calorimeter), into a measured mass of cool water; record the temperature rise and the mass of steam condensed.
• Calculation: heat released by the condensing and cooling steam = heat gained by the water and container; use this to find L for steam.
• Sources of error: without a steam trap, condensed water droplets carried over with the steam would add extra mass without releasing the full latent heat, giving an inaccurate result.

• Measure the mass of the empty calorimeter and the mass of calorimeter plus liquid, so the liquid mass is found by subtraction. Record initial and final temperatures and the electrical energy supplied by a joulemeter.
• Use: electrical energy supplied = heat gained by liquid + heat gained by calorimeter. Therefore Q = m_liquidc_liquidΔθ + m_calc_calΔθ.
• Begin about 5 °C below room temperature and finish about 5 °C above it where practical. This helps the heat gained from the room early in the run approximately balance heat lost later.
• Keep the heating coil fully covered, stir continuously, and use a temperature rise large enough to keep the percentage uncertainty in Δθ small.

• Fusion of ice: heat lost by warm water and calorimeter = energy to melt the ice + energy to warm the melted ice from 0 °C to the final temperature.
• Vaporisation of water: heat lost as steam condenses + heat lost as the condensate cools from 100 °C = heat gained by water and calorimeter.
• Use masses found by subtraction, convert grams to kilograms, keep every term in joules, and state why the ice is dried or the steam trap is used.

• Specific heat capacity: use a DC supply with the ammeter and immersion heater in series, and connect the voltmeter directly across the heater. Measure the heating time with a stopwatch. If a joulemeter is used, connect it as a measuring device between the supply and heater; it does not replace the power supply.
• Use E = VIt for electrical energy supplied and Q = mcΔT for thermal energy gained. V is the potential difference across the heater, I is the current through it, t is heating time, m is the mass heated, c is specific heat capacity and ΔT is the temperature rise.
• Set E ≈ Q only when energy absorbed by the container, heater and thermometer and energy lost to the surroundings are negligible or have been accounted for.
• Fusion: dry the ice and account for warming the melted ice. Vaporisation: use dry steam and account for cooling the condensate.
• Insulate, stir, repeat and apply a cooling correction where appropriate. Use heat-resistant equipment and protect against hot water/steam.

• Use supplied energy–temperature data for both a solid and a liquid. For each dataset, find the gradient of energy Q against temperature rise Δθ; since gradient = mc, divide by mass to obtain c.
• Compare the results with accepted values and evaluate heat loss, container heat capacity, sensor lag and measurement uncertainty.
• The specification requires primary determination for either a solid or liquid and secondary-data treatment for both.

Quick-Check Questions

Short retrieval questions covering the essential ideas in Temperature and Heat Transfer.

1. Convert 15 °C to kelvin.

2. Why does temperature stay constant while a substance is melting or boiling, even though heat is still being supplied?

3. Name the three modes of heat transfer and state which one(s) can occur through a vacuum.

4. Why is a dull black surface a better emitter of thermal radiation than a shiny surface?

5. What does a lower U-value tell you about a material?

Common mistakes and exam tips

Common misconceptions and exam-technique checks for Temperature and Heat Transfer.

• Avoid: Using “heat contained in an object” as a synonym for temperature. Correct idea: Temperature describes thermal state; heat is energy transferred because of a temperature difference.
• Avoid: Using Q = mcΔθ during melting or boiling. Correct idea: During a change of state at constant temperature, use Q = mL.
• Avoid: Saying conduction or convection transfers energy through a vacuum. Correct idea: Only thermal radiation can transfer energy through a vacuum.

• Separate multi-stage heating problems into warming and change-of-state stages.
• Use the latent heat and specific heat capacity for the correct substance and phase.
• A temperature interval has the same numerical size in kelvin and degrees Celsius.

Exam-style questions

Five exam-style questions with worked answers on Temperature and Heat Transfer.

Higher Level — Required Content

Required Higher Level content for this topic.

Specific latent heat is the thermal energy required to change the state of 1 kg of a substance without a change in temperature.

• Use the appropriate value for fusion or vaporisation.
• During the change of state, temperature remains constant while energy changes the internal arrangement of the particles.
• In an investigation, determine L from the measured energy transferred and mass that changes state.

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for Temperature and Heat Transfer.

Try without notes: sketch a heating curve for ice to steam, and state which sections use Q = mcΔθ and which use Q = mL.

• θ(°C) = T(K) − 273.15; T(K) = θ(°C) + 273.15
• C = Q/Δθ
• c = Q/(mΔθ), so Q = mcΔθ
• L = Q/m, so Q = mL
• Rate of heat loss = U A Δθ

• Temperature vs heat energy
• Specific heat capacity
• Specific latent heat (fusion and vaporisation)
• Conduction, convection, radiation
• U-value

• A labelled heating curve showing plateaus at melting and boiling points
• Conduction/convection/radiation particle-model sketches, including dull vs shiny surfaces for radiation

• Measuring the specific heat capacity of water or a solid
• Measuring the specific latent heat of fusion of ice (using dried ice)
• Measuring the specific latent heat of vaporisation of water (using a steam trap for dry steam)

• Temperature vs heat energy confusion
• Saying absolute zero means 'no heat energy'
• Applying Q = mcΔθ during a change of state instead of Q = mL
• Thinking convection or conduction can occur through a vacuum

1. Convert 350 K to degrees Celsius.

2. A 1.5 kg block of metal (c = 900 J kg⁻¹ K⁻¹) cools from 80 °C to 20 °C. Calculate the heat energy released.

3. Explain why a steam trap is used when measuring the specific latent heat of vaporisation of water.

4. Explain why metals feel colder to the touch than wood at the same room temperature.

1. θ(°C) = T(K) − 273.15 = 350 − 273.15 = 76.85 °C.

2. Q = mcΔθ = 1.5 × 900 × (80−20) = 1.5 × 900 × 60 = 81 000 J = 8.1 × 10⁴ J.

3. A steam trap removes water droplets carried along with the steam, ensuring only dry steam (not a mix of steam and already-condensed water) enters the calorimeter — without it, the extra droplet mass would be wrongly counted as steam that released its full latent heat, giving an inaccurate result for L.

4. Metals are much better conductors of heat than wood, so they conduct heat away from your hand much faster, making them feel colder even though both are at the same actual temperature.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.

Note: the new Leaving Certificate Physics specification's own content list confirms heat capacity, specific heat capacity, specific latent heat, the concept of a heat pump, and U-value as the rate of heat transfer through a material — matching the core content of this unit.