4.1.2Properties of Matter
Calculating Specific Heat Capacity
5 min read 5 parts Lesson 2 of 11
Section 1 of 5The Equation
One equation links heat energy to the properties of the material.
Relationship
- Eh = cmΔT, where Eh is the heat energy in joules, c is specific heat capacity, m is mass in kg and ΔT is the temperature change.
Temperature change
- Find ΔT by subtracting the initial temperature from the final temperature.
Rearranged
- c = Eh ÷ (mΔT) finds the specific heat capacity, and ΔT = Eh ÷ (cm) finds the temperature rise.
Mass units
- Convert grams to kilograms before substituting, for example 500 g = 0.50 kg.
| Symbol | Quantity | Unit |
|---|---|---|
| Eh | Heat energy | J |
| c | Specific heat capacity | J/kg °C |
| m | Mass | kg |
| ΔT | Temperature change | °C |
Section 2 of 5Experiment to Find c
An electric heater can supply a known amount of energy to a solid block.
1
Measure the mass of a metal block and place a heater and a thermometer in holes drilled into it.
2
Wrap the block in insulation, then record the starting temperature.
3
Switch on the heater for a measured time and note the power rating or use a joulemeter.
4
Calculate the energy supplied from Eh = Pt and record the final temperature.
5
Use c = Eh ÷ (mΔT) to calculate the specific heat capacity of the metal.
Section 3 of 5Sources of Error
Not all the energy supplied heats the block, which affects the result.
Sources of Error
Heat losses
- Some energy escapes to the surroundings, so the energy actually absorbed is less than the energy supplied.
Effect on c
- Using the full energy supplied makes the calculated value of c larger than the true value.
Improvement
- Insulating the block with lagging reduces heat loss and gives a result closer to the accepted value.
Good practice
- Use a drop of oil in the thermometer hole and stir liquids so the temperature is the same throughout.
Section 4 of 5Worked Example
Question
- A 50 W heater warms a 0.50 kg aluminium block for 3.0 minutes and the temperature rises by 20 °C.
- Calculate the specific heat capacity of the block.
- Energy supplied Eh = Pt = 50 × 180 = 9000 J.
- Rearrangec = Eh ÷ (mΔT).
- c = 9000 ÷ (0.50 × 20) = 900 J/kg °C.
Answer
- The specific heat capacity is 900 J/kg °C.
- (For comparison, heating 2.0 kg of water by 15 °C needs 4180 × 2.0 × 15 = 125 400 J.)
Section 5 of 5Exam Checklist & Tips
4.1.2 – Key Points for the Exam
- Eh = cmΔT The equation for heat energy needed to change a temperature.
- ΔT The change in temperature, in degrees Celsius.
- Lagging Insulating material that reduces heat loss.
- Power
- Rate of energy transfer;
- Eh = Pt gives the energy from a heater.
- Rate of energy transfer;
Common Mistakes
- Using the final temperature instead of the temperature change.
- Leaving the mass in grams.
- Forgetting that heat losses make the calculated value of c too high.
- Rearranging the equation incorrectly, for example c = mΔT ÷ Eh.