Internal energy, \$U\$, is the total energy stored inside a system. It comes from two main sources:
When you heat an object, you add energy to it. That energy increases the motion of its molecules, raising the temperature. The relationship is:
\$\Delta U = m\,c\,\Delta T\$
where \$m\$ is mass, \$c\$ is specific heat capacity, and \$\Delta T\$ is the change in temperature.
Imagine a hot water bottle. The water molecules move faster when heated, so the bottle feels warmer. The energy that makes the water molecules move faster is the internal energy. The hotter the water, the higher the internal energy.
Different materials store heat differently. The specific heat capacity tells us how much energy is needed to raise 1 kg of a substance by 1 °C.
| Material | \$c\$ (J kg⁻¹ K⁻¹) |
|---|---|
| Water | 4184 |
| Aluminium | 900 |
| Iron | 450 |
When you see a question about how much energy is required to heat a metal block, remember to:
Always show your work and keep track of units!
Heat capacity \$C\$ is the energy needed to raise the temperature of a whole object by 1 °C:
\$C = \frac{\Delta U}{\Delta T}\$
For a uniform material, \$C = m\,c\$. So if you know the mass and the specific heat capacity, you can find the heat capacity.
How much energy is needed to raise a 2 kg aluminium block from 20 °C to 80 °C?
Given \$c_{\text{Al}} = 900\$ J kg⁻¹ K⁻¹ and \$\Delta T = 60\$ °C:
\$\Delta U = 2\,\text{kg} \times 900\,\frac{\text{J}}{\text{kg·K}} \times 60\,\text{K} = 108{,}000\,\text{J}\$
So you need 108 kJ of energy.
Increasing the temperature of an object always increases its internal energy because the molecules move faster or vibrate more. The exact amount depends on the material’s specific heat capacity.
1. A 0.5 kg iron rod is heated from 25 °C to 125 °C. Calculate the change in internal energy.
2. Explain why water has a higher specific heat capacity than iron.
Use the formula and the values given in the table above.