Heat Capacity & Specific Heat Capacity

1. Definition

A. Heat capacity

Heat capacity, C, of a body is the energy required to raise its temperature by 1 K (or 1°C), without change of state.

C = Q/(Δ θ)

B. Specific heat capacity

Specific heat capacity, c, of a substance is the energy required to raise the temperature of 1 kg of the substance by 1 K (or 1°C), without change of state.

Q = mcΔ θ

2. Key Ideas

• Units:
  • C in J K⁻¹ (or J °C⁻¹)
  • c in J kg⁻¹ K⁻¹ (or J kg⁻¹ °C⁻¹)
  • Q in J, m in kg, Δ θ in K or °C
• Temperature changes: 1 K is the same size as 1°C, so you can use Δ θ in either unit.
• Rearrangements:
  • Q = CΔ θ
  • c = Q/(mΔ θ)
  • C = mc
• For the same energy input Q:
  • larger m or larger c → smaller temperature rise (Δ θ).

3. Detailed Explanations

A. Heat capacity vs specific heat capacity

• Heat capacity C applies to a particular object (depends on its mass and material).
• Specific heat capacity c is a property of the material (per kilogram).

They are linked by:

C = mc

So a larger mass of the same material has a larger heat capacity.

B. What does “high specific heat capacity” mean?

If a material has a high c:

• it needs a lot of energy to raise its temperature by 1°C per kg
• for the same heating power, it warms up more slowly
• under otherwise identical cooling conditions, its temperature changes more slowly

C. Measuring the specific heat capacity of a metal block

1. Measure the block’s mass m with a balance.
2. Insert the heater and thermometer into their holes. Add a little thermal-contact material if instructed, so air gaps do not slow energy transfer.
3. Wrap the block in insulation and record its initial temperature.
4. Connect an ammeter in series with the heater and a voltmeter across it. Switch on and record I, V and heating time t.
5. Record the final temperature and calculate Δθ.

The electrical energy supplied is E = VIt (or E = Pt if power is measured). Under the ideal assumption that all of it raises the block’s internal energy,

c = VIt/mΔθ.

D. A stronger data method

Record temperature at regular times while V and I are approximately constant, then plot temperature against time. The early gradient can be used with VI ≈ mc(Δθ/Δ t). Repeated readings reveal anomalies and make the trend more reliable than a single start–finish pair, although heat loss still needs evaluation.

4. Common Mistakes

• Using mass in g instead of kg without converting.
• Using the absolute temperature instead of the temperature change (use Δ θ).
• Forgetting the “no change of state” condition (during melting/boiling, this formula is not used).
• Mixing up C (heat capacity) with c (specific heat capacity).
• Writing units incorrectly (e.g. missing kg⁻¹ for c).
• Claiming insulation removes all heat loss. It reduces unwanted transfer; it does not make it zero.
• Putting the voltmeter in series or the ammeter across the heater.

5. Exam Tips

• Write the equation first, then substitute values with units:
  • Q = mcΔθ or C = Q/Δθ
• Convert mass to kg and temperature change to K or °C.
• If the question gives power and time, use:
  • Q = Pt
• If the question mentions “assume no heat loss”, state it explicitly before using Q = Pt.
• In an evaluation question, name the energy destination and its effect on the result; “heat loss causes error” is too vague.

6. Worked Examples

7. Mind Stretchers

8. Practice and next step

Check mass conversion, Δθ and units in the Thermal Physics quiz, then show full working in structured practice. Continue to melting and solidification, where energy can transfer without a temperature change.