TL;DR Specific heat capacity c is the energy needed to raise 1 kg of a substance by 1 K (or 1 °C). The syllabus expects three methods: the electrical method for a solid, the electrical method for a liquid, and the method of mixtures. All three rely on the same core equation: Q=mcΔT. Most marks are lost by forgetting to insulate the apparatus, not stirring the liquid, or mixing up signs in the heat-balance equation.
For marking priorities and examiner expectations, pair this walkthrough with the Paper 3 Marking Guide.
1 | What specific heat capacity is
Specific heat capacity is the amount of thermal energy required to raise the temperature of one kilogram of a substance by one kelvin (or equivalently, one degree Celsius).
The defining equation is:
Q=mcΔT
Reviewed by
Chee Wei Jie·Academic Advisor (Physics)
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Different substances have different specific heat capacities. Water, for example, has a high specific heat capacity of about 4200 J kg−1 K−1, which is why it takes a long time to boil and why it is used as a coolant. Aluminium has a lower value of roughly 900 J kg−1 K−1.
2 | Method 1 - Electrical method for a solid block
Apparatus
Item
Purpose
Metal block (e.g. aluminium or copper) with two drilled holes
One hole accepts the immersion heater; the other accepts the thermometer.
Electric immersion heater
Supplies a known amount of electrical energy to the block.
Joulemeter (or ammeter + voltmeter + stopwatch)
Measures the electrical energy delivered. If no joulemeter is available, use E=VIt. For help wiring the ammeter and voltmeter, see the ammeter and voltmeter connection guide.
Thermometer (0--110 °C) or temperature sensor
Measures the temperature of the block before and after heating.
Electronic balance
Measures the mass of the metal block.
Insulating material (e.g. cotton wool, polystyrene jacket)
Reduces heat loss from the block to the surroundings.
Oil or water in the thermometer hole
Improves thermal contact between the thermometer and the block.
Step-by-step method
Measure and record the mass of the metal block using the balance. Record m in kg.
Insert the heater into one hole and the thermometer into the other. Add a few drops of oil into the thermometer hole to ensure good thermal contact.
Wrap the block in insulating material to minimise heat loss.
Record the initial temperatureθ1 of the block.
Switch on the heater. If using a joulemeter, record its initial reading J1. If using an ammeter and voltmeter, record the current I, the voltage V, and start the stopwatch.
Heat for a measured time (typically 5--10 minutes) until the temperature has risen by about 10--20 °C.
Switch off the heater. Record the final joulemeter reading J2 (or the elapsed time t). Wait about 30 seconds for the temperature to stabilise, then record the maximum temperature θ2.
Calculate the electrical energy supplied:
Q=J2−J1(joulemeter)
or
Q=VIt(ammeter + voltmeter + stopwatch)
Calculate the specific heat capacity:
c=m(θ2−θ1)Q
Data table template
Quantity
Value
Mass of block, m / kg
Initial temperature, θ1 / °C
Final temperature, θ2 / °C
Temperature rise, Δθ / °C
Joulemeter start, J1 / J
Joulemeter end, J2 / J
Energy supplied, Q / J
3 | Method 2 - Electrical method for a liquid
Apparatus
Item
Purpose
Calorimeter (thin-walled metal cup, often copper or aluminium)
Contains the liquid and has good thermal conductivity.
Lid for the calorimeter
Reduces heat loss through evaporation and convection from the top.
Stirrer (glass or metal rod)
Ensures the liquid has a uniform temperature throughout.
Electric immersion heater
Supplies electrical energy to the liquid.
Joulemeter (or ammeter + voltmeter + stopwatch)
Measures the electrical energy delivered.
Thermometer (0--110 °C)
Measures the temperature of the liquid.
Electronic balance
Measures the mass of the liquid (by difference: filled calorimeter minus empty calorimeter).
Insulating jacket or lagging
Surrounds the calorimeter to reduce heat loss.
Step-by-step method
Measure the mass of the empty calorimetermcal. Then pour in the liquid and measure the combined mass. The mass of the liquid is:
mliquid=mtotal−mcal
Assemble the apparatus. Place the heater and thermometer into the liquid through the lid. Surround the calorimeter with insulating lagging.
Record the initial temperatureθ1.
Switch on the heater and record the joulemeter start reading J1 (or note V, I, and start the stopwatch). Stir the liquid continuously.
Heat for a set time (typically 5--10 minutes) until the temperature has risen by about 10--15 °C. Stir throughout.
Switch off the heater. Record J2 (or elapsed time t). Continue stirring and record the maximum temperature θ2.
Calculate the energy supplied using Q=J2−J1 or Q=VIt
Calculate the specific heat capacity of the liquid. If you ignore the heat absorbed by the calorimeter:
cliquid=mliquid×ΔθQ
For a more accurate result (required if the question states it), account for the calorimeter:
Q=mliquidcliquidΔθ+mcalccalΔθ
Rearranging:
cliquid=mliquid×ΔθQ−mcalccalΔθ
Data table template
Quantity
Value
Mass of empty calorimeter, mcal / kg
Mass of calorimeter + liquid / kg
Mass of liquid, mliquid / kg
Initial temperature, θ1 / °C
Final temperature, θ2 / °C
Temperature rise, Δθ / °C
Energy supplied, Q / J
4 | Method 3 - Method of mixtures
The method of mixtures does not use an electrical heater. Instead, a hot solid is transferred into cold water and thermal energy flows from the solid to the water until both reach a common final temperature.
Apparatus
Item
Purpose
Metal specimen (e.g. copper, iron, or lead block)
The solid whose specific heat capacity you want to find.
Boiling water bath (beaker on a tripod/gauze)
Heats the solid to a known high temperature (approximately 100 °C).
Calorimeter with lid and stirrer
Contains the cold water and receives the hot solid.
Thermometer (two ideally: one for the water bath, one for the calorimeter)
Measures temperatures of the hot solid and the cold water.
Electronic balance
Measures masses of the solid and the water.
Thread or tongs
Transfers the hot solid quickly into the cold water.
Insulating jacket
Reduces heat loss from the calorimeter during mixing.
Step-by-step method
Measure the mass of the metal specimenms.
Suspend the specimen in a boiling water bath for several minutes until it reaches thermal equilibrium with the boiling water. Record the temperature of the boiling water as θhot (close to 100 °C).
Pour a known mass of cold watermw into the calorimeter. Record the initial temperature of the water θcold.
Transfer the hot solid quickly into the cold water. Minimise the transfer time to reduce heat loss during the move.
Replace the lid, stir continuously, and record the highest temperature reached by the mixture θmix.
Apply the heat-balance equation. Assuming no heat loss to the surroundings:
heat lost by solid=heat gained by water
mscs(θhot−θmix)=mwcw(θmix−θcold)
Rearranging for cs:
cs=ms(θhot−θmix)mwcw(θmix−θcold)
5 | Worked example - electrical method for a solid
A student heats an aluminium block using an electrical heater. The data collected are:
Mass of aluminium block: m=1.00 kg
Initial temperature: θ1=22.0 °C
Final temperature: θ2=34.5 °C
Ammeter reading: I=4.0 A
Voltmeter reading: V=12.0 V
Heating time: t=300 s
Step 1 - Calculate the energy supplied:
Q=VIt=12.0×4.0×300=14,400 J
Step 2 - Calculate the temperature rise:
Δθ=34.5−22.0=12.5 °C
Step 3 - Calculate the specific heat capacity:
c=mΔθQ=1.00×12.514,400=1152 J kg−1 K−1
Step 4 - Compare with the accepted value:
The accepted specific heat capacity of aluminium is about 900 J kg−1 K−1. The experimental value is higher than expected. This indicates that some electrical energy was lost as heat to the surroundings rather than being used to raise the temperature of the block, so the denominator (mΔθ) is smaller than it should be, making the calculated c too large.
6 | Sources of error and improvements
For the thermal section of our per-experiment error bank (heat loss, thermometer lag, evaporation, calorimeter heat capacity), see the O-Level Physics sources of error guide.
Source of error
Effect
Improvement
Heat loss from the block or calorimeter to the surroundings
Not all supplied energy goes into raising the temperature of the specimen. The calculated c will be too high (electrical method) or too low (method of mixtures for the solid).
Wrap the apparatus in insulating lagging. Use a lid on the calorimeter.
Incomplete thermal equilibrium
The thermometer may not read the true temperature of the block or the mixture.
Wait for the temperature reading to stabilise before recording.
Thermometer lag
The thermometer responds slowly, so the recorded peak temperature may be lower than the actual peak.
Use a digital temperature sensor with a faster response time.
No stirring (liquid experiments)
Temperature is not uniform throughout the liquid, leading to an inaccurate Δθ.
Stir the liquid continuously throughout the experiment.
Evaporation of liquid
Energy is used for the latent heat of vaporisation rather than raising the temperature, giving a higher apparent c.
Use a lid on the calorimeter to reduce evaporation.
Slow transfer of hot solid (method of mixtures)
The solid cools during the transfer, so the effective θhot is lower than recorded, giving an underestimate of cs.
Transfer the solid as quickly as possible. Minimise the distance between the boiling bath and the calorimeter.
Ignoring the heat capacity of the calorimeter
The calorimeter itself absorbs some energy, leading to an overestimate of the liquid's c.
Include mcalccalΔθ in the energy balance equation.
7 | Graph skills - temperature vs time
Some variants of this experiment ask you to record temperature at regular time intervals while the heater runs at constant power. This produces a temperature--time (θ--t) graph.
What to plot
x-axis: time t / s
y-axis: temperature θ / °C
How to find the rate of temperature rise
Draw the best-fit straight line through the linear portion of the graph. The gradient gives the rate of temperature rise:
gradient=ΔtΔθ(°C s−1)
Because the heater delivers energy at a constant rate (power P):
P=mc×ΔtΔθ
Rearranging:
c=m×gradientP
This graphical method averages out random errors across all your data points, giving a more reliable result than using just two temperature readings.
Mistake 1 - Forgetting to convert mass to kilograms
The formula c=Q/(mΔT) requires mass in kilograms. If the question gives the mass in grams (e.g. 200 g), you must convert to 0.200 kg before substituting. Failing to convert gives a value of c that is 1000 times too small.
Mistake 2 - Not accounting for the heat capacity of the calorimeter
When the question provides mcal and ccal, you must include the energy absorbed by the calorimeter. Omitting the calorimeter term inflates the calculated c of the liquid.
Mistake 3 - Wrong sign in the method of mixtures equation
A common error is writing "heat lost = heat gained" but then subtracting temperatures in the wrong order. Remember:
Heat lost by the hot object: mscs(θhot−θmix) - the higher temperature comes first.
Heat gained by the cold water: mwcw(θmix−θcold)
Both expressions must be positive.
Mistake 4 - Not waiting for thermal equilibrium
In the method of mixtures, the final temperature is the highest steady reading after stirring, not the temperature the instant the solid is dropped in. In the electrical method, the block temperature may continue to rise slightly after the heater is switched off (thermal lag), so wait for the reading to peak and stabilise.
Mistake 5 - Stating vague sources of error
"Human error" or "equipment not accurate" earns zero marks. Be specific: state what physical process causes the error (e.g. heat loss through the uninsulated surface) and what effect it has on the result (e.g. c is overestimated because not all energy goes into heating the block).
Mistake 6 - Using ΔT = final temperature only
The temperature rise ΔT is the difference between the final and initial temperatures, not the final temperature alone. A student who records θ2=45 °C and uses 45 in the formula instead of 45−25=20 °C will get a wildly incorrect answer.
9 | Frequently asked questions
What is the difference between heat capacity and specific heat capacity?
Heat capacity is the energy needed to raise the temperature of an entire object by 1 K. Specific heat capacity is the energy needed per kilogram per kelvin. The relationship is: heat capacity C=mc, where m is the mass and c is the specific heat capacity.
Why do we add oil to the thermometer hole in the metal block?
Air is a poor conductor of heat. A thin air gap between the thermometer and the block wall means the thermometer does not read the true block temperature. Oil fills this gap and provides better thermal contact, giving a more accurate temperature reading.
Can I use Celsius or must I use Kelvin?
For temperature changes (ΔT), Celsius and Kelvin give the same numerical value because the scale divisions are the same size. You do not need to convert to Kelvin for specific heat capacity calculations - unlike Charles' Law, where absolute temperature is required.
Why is the experimental value of c usually higher than the accepted value?
In the electrical method, some energy escapes to the surroundings instead of heating the block or liquid. The energy input Q is therefore larger than the energy actually absorbed by the substance, so dividing by mΔT gives a value of c that is too high.
What equipment is needed for a specific heat capacity experiment?
At minimum: a heater (electrical immersion heater or boiling water bath), a thermometer, a balance, and insulating material. For the electrical method you also need a joulemeter or an ammeter, voltmeter, and stopwatch. For the method of mixtures you need a calorimeter with a lid and stirrer.
How does the method of mixtures differ from the electrical method?
The electrical method measures energy input directly (via a joulemeter or E=VIt). The method of mixtures uses no electricity; instead it relies on the principle that heat lost by a hot object equals heat gained by cold water, so the known c of water acts as the reference.
