Define specific heat capacity as the energy required per unit mass per unit temperature increase; recall and use the equation c = ΔE / m Δθ

2.2.2 Specific Heat Capacity

1. Syllabus Context

This sub‑topic belongs to Section 2 – Thermal Physics of the Cambridge IGCSE Physics (0625) syllabus. It follows the kinetic particle model, states of matter and the ideal‑gas law, and precedes the sections on thermal expansion, latent heat and heat‑transfer mechanisms.

2. Definition, Physical Meaning & Key Equation

Specific heat capacity (c) is the amount of energy required to raise the temperature of 1 kg of a substance by 1 °C (or 1 K). The supplied energy becomes thermal (internal) energy of the material, increasing the average kinetic energy of its particles.

Mathematically:

where

• \(\Delta E\) = energy supplied (J)
• \(m\) = mass of the substance (kg)
• \(\Delta T = T{2}-T{1}\) = temperature change (°C or K)

Re‑arranging gives the working form used in calculations:

3. Units

• SI unit: joule per kilogram per kelvin (J kg⁻¹ K⁻¹).
• Because a temperature change of 1 °C equals 1 K, the unit is often written J kg⁻¹ °C⁻¹.

4. Typical Values of Specific Heat Capacity

5. Derivation from the Definition

1. Start with the definition: energy required per unit mass per unit temperature change.
2. Write it as a ratio: \(\displaystyle c = \frac{\text{energy required}}{\text{mass}\times\text{temperature change}}\).
3. Cross‑multiply to isolate the energy term, giving the practical formula: \(\displaystyle \Delta E = c\,m\,\Delta T.\)

6. Why Specific Heat Capacities Differ – Particle‑Model Explanation

• Specific heat capacity reflects how much energy is needed to increase the average kinetic energy of the particles.
• Materials with strong intermolecular forces (e.g., water) must first overcome these forces before particle speeds increase, giving a high \(c\).
• Metals have a lattice of free electrons that can store energy with relatively little temperature rise, so they have lower \(c\) values.
• Gases have many degrees of freedom (translation, rotation, vibration) and a low mass per unit volume, resulting in moderate \(c\) values (≈ 1000 J kg⁻¹ K⁻¹ for air).

7. Worked Example

Problem: How much energy is needed to raise the temperature of 250 g of water from 20 °C to 80 °C?

1. Identify the data

   • Mass, \(m = 250\ \text{g} = 0.250\ \text{kg}\)
   • Initial temperature, \(T_{1}=20\ ^\circ\text{C}\)
   • Final temperature, \(T_{2}=80\ ^\circ\text{C}\)
   • Temperature change, \(\Delta T = T{2}-T{1}=60\ ^\circ\text{C}=60\ \text{K}\)
   • Specific heat capacity of water, \(c = 4180\ \text{J kg}^{-1}\text{K}^{-1}\)

2. Apply the formula

   \[

   \Delta E = c\,m\,\Delta T = 4180 \times 0.250 \times 60 = 6.27 \times 10^{4}\ \text{J}

   \]

3. Answer: \(\displaystyle 6.27 \times 10^{4}\ \text{J}\) of energy must be supplied.

8. Common Misconceptions

• Specific heat capacity vs. heat capacity – Heat capacity (\(C\)) refers to the energy required for an entire object; specific heat capacity (\(c\)) is per kilogram.
• Mass units – The equation uses kilograms. Convert grams or milligrams to kg before substituting.
• Temperature scales – A change of 1 °C is identical to a change of 1 K, but absolute temperatures differ. Use \(\Delta T\) (change), not the absolute temperature.
• Sign of \(\Delta T\) – If a substance cools, \(\Delta T\) is negative, giving a negative \(\Delta E\) (energy released).

9. Experimental Determination of Specific Heat Capacity

9.1 Solid (metal) – Calorimetry Method

1. Heat a known mass of the metal in boiling water (≈ 100 °C).
2. Transfer it quickly into a known mass of water at a measured initial temperature inside an insulated calorimeter.
3. Record the highest (final) temperature reached.
4. Assuming no heat loss, use

   \[

   c{\text{metal}} = \frac{c{\text{water}}\,m{\text{water}}\,(Tf-T{i,\text{water}})}{m{\text{metal}}\,(T{i,\text{metal}}-Tf)}

   \]

   to calculate \(c_{\text{metal}}\).

9.2 Liquid (water) – Electrical‑Heater Calorimeter

1. Place a known mass of water in an insulated container equipped with an electrical heater and a thermometer.
2. Pass a known current \(I\) for a measured time \(t\) through the heater of voltage \(V\); the electrical energy supplied is \(E = V I t\) (or \(E = P t\) with \(P = VI\)).
3. Measure the temperature rise \(\Delta T\) of the water.
4. Calculate the specific heat capacity of water using

   \[

   c{\text{water}} = \frac{E}{m{\text{water}}\Delta T}.

   \]

10. Practical Activity (AO3 – Skills)

Combine the two methods above in a single lab session: determine \(c\) for an unknown metal and verify the accepted value for water using the electrical‑heater calorimeter. Record all masses, temperatures, currents, voltages and times, and propagate uncertainties to assess experimental reliability.

11. Practice Questions

1. A 1.5 kg block of aluminium (\(c = 900\ \text{J kg}^{-1}\text{K}^{-1}\)) is heated from 25 °C to 75 °C. Calculate the energy supplied.
2. How much will the temperature of 500 g of copper (\(c = 385\ \text{J kg}^{-1}\text{K}^{-1}\)) increase if it absorbs 10 kJ** of energy?
3. Compare the energy required to raise 1 kg of water and 1 kg of iron (\(c = 450\ \text{J kg}^{-1}\text{K}^{-1}\)) by 10 K. Which needs more energy and why?

12. Suggested Diagram