How Do You Calculate Energy Needed for a Temperature Change (Q = mcΔT)?

Use $Q=mc\Delta T$: multiply the object's mass by its specific heat capacity and its temperature change. This relationship belongs to B.1 Thermal energy transfers and applies to both SL and HL IB Physics.

The Reasoning

Specific heat capacity $c$ is the energy required to increase the temperature of $1\,\text{kg}$ of a substance by $1\,\text{K}$. Therefore,

$$Q=mc\Delta T$$

where $\Delta T=T_{\text{final}}-T_{\text{initial}}$.

A temperature change has the same numerical value in kelvin and Celsius degrees. For example, heating from $20\,°\text{C}$ to $80\,°\text{C}$ gives $\Delta T=60\,\text{K}$. However, equations requiring absolute temperature, such as the ideal gas equation, must use kelvin.

Worked Example

Calculate the energy needed to heat $0.50\,\text{kg}$ of water from $20\,°\text{C}$ to $80\,°\text{C}$, taking $c=4200\,\text{J kg}^{-1}\text{K}^{-1}$.

$$\Delta T=80-20=60\,\text{K}$$ $$Q=(0.50)(4200)(60)=126000\,\text{J}=1.26\times10^5\,\text{J}$$

Therefore, $126\,\text{kJ}$ of energy must be transferred to the water. The unit check confirms the result: $\text{kg}\times\text{J kg}^{-1}\text{K}^{-1}\times\text{K}=\text{J}$.

If an object cools, $\Delta T<0$, so $Q<0$ when $Q$ means energy transferred to the object. Its magnitude gives the energy transferred from the object.

The equation assumes no phase change and a known, approximately constant specific heat capacity over the temperature range. In experiments, energy may also heat the container or escape to the surroundings, so the electrical energy supplied can exceed the energy gained by the substance. Unless stated otherwise, IB calculations usually treat the system as thermally isolated.

A common misconception is applying $Q=mc\Delta T$ during a phase change. During melting or boiling, temperature remains constant, so use $Q=mL$, where $L$ is specific latent heat. If heating includes both temperature changes and a phase change, calculate each stage separately and add the energy transfers.

Exam Technique

For a Calculate question, show the equation, calculate $\Delta T$, substitute values, and state the final answer. Convert grams to kilograms, distinguish temperature change from final temperature, and select the specific heat capacity of the correct substance.