Specific Heat Capacity | CAIE 9702 Paper 4 Notes

Chapters

Paper 4

Physics9702

Specific Heat Capacity

Two objects can receive the same energy but have different temperature rises. Their masses and materials both matter.

Energy needed for one kilogram and one kelvin

The material property is its .

Definition

2 marks

What is meant by specific heat capacity?

Model answer: The thermal energy needed per unit mass to raise the temperature of a substance by one kelvin.

A high specific heat capacity means that more energy is needed for the same mass and temperature rise (9702/41/O/N/24 Q2(a)).
For the same energy and mass, a material with a higher specific heat capacity has a smaller temperature rise.
The equation below applies when the substance stays in the same state. Use the final temperature minus the initial temperature.

Q=mc\Delta\theta

Symbols

$Q$ = thermal energy transferred (J)
$m$ = mass (kg)
$c$ = specific heat capacity (J kg⁻¹ K⁻¹)
$\Delta\theta$ = temperature change (K or °C)

\Delta\theta=\theta_{\mathrm{final}}-\theta_{\mathrm{initial}}

Swipe left or right to see the whole diagram →

For the same mass and energy input, the material with the smaller specific heat capacity has the larger temperature rise.

Worked example

Find a specific heat capacity

A 2.0 kg aluminium block receives 26 400 J. Its temperature rises by 15 K. Find its specific heat capacity.

Rearrange the energy equation.
$c=\dfrac{Q}{m\Delta\theta}$
Substitute the values.
$c=\dfrac{26400}{2.0\times15}$
$c=880\ \mathrm{J\,kg^{-1}\,K^{-1}}$

Answer

c=880\ \mathrm{J\,kg^{-1}\,K^{-1}}

Your turnquick check

Equal masses of two materials receive the same energy. Material A has the larger temperature rise. Which material has the smaller specific heat capacity?

Show worked answer

Material A. A smaller specific heat capacity gives a larger temperature rise for the same mass and energy.