Describe experiments to measure the specific heat capacity of a solid and a liquid

2.2.2 Specific Heat Capacity

What is Specific Heat Capacity?

🔬 Specific heat capacity ($c$) is the amount of heat required to raise the temperature of 1 g of a substance by 1 °C (or 1 K). It tells us how “heat‑resistant” a material is. Think of it like a sponge: a sponge that absorbs a lot of water before getting wet is like a substance with a high $c$; a sponge that gets wet quickly has a low $c$.

Formula

The heat added or removed is given by $$Q = mc\Delta T$$ where $m$ = mass (g), $c$ = specific heat capacity (J g⁻¹ °C⁻¹), $\Delta T$ = change in temperature (°C). Rearranging gives $$c = \frac{Q}{m\Delta T}$$.

Measuring the Specific Heat of a Solid

⚗️ Calorimeter Method – a simple way to find $c$ for a solid (e.g., a metal block).

  1. Heat the solid in a small oven or hot plate to a known temperature $T_{\text{solid}}$.
  2. Measure its mass $m_{\text{solid}}$ with a balance.
  3. Place the hot solid into a calorimeter filled with a known mass of water $m_{\text{water}}$ at room temperature $T_{\text{water}}$.
  4. Let the system reach equilibrium; record the final temperature $T_{\text{final}}$.
  5. Assume no heat loss to the surroundings. The heat lost by the solid equals the heat gained by the water: $$m_{\text{solid}}c_{\text{solid}}(T_{\text{solid}}-T_{\text{final}})=m_{\text{water}}c_{\text{water}}(T_{\text{final}}-T_{\text{water}})$$
  6. Rearrange to solve for $c_{\text{solid}}$: $$c_{\text{solid}}=\frac{m_{\text{water}}c_{\text{water}}(T_{\text{final}}-T_{\text{water}})}{m_{\text{solid}}(T_{\text{solid}}-T_{\text{final}})}$$
Exam Tip: • Always convert masses to grams and temperatures to °C (or K). • Use $c_{\text{water}} = 4.18$ J g⁻¹ °C⁻¹. • Check that $T_{\text{solid}} > T_{\text{final}} > T_{\text{water}}$ to avoid sign errors. • Remember that heat lost by the solid is positive in the equation above.

Measuring the Specific Heat of a Liquid

🧪 Direct Heating Method – often used for liquids like alcohol or water.

  1. Measure a known volume $V$ of the liquid and calculate its mass $m_{\text{liquid}}$ using its density.
  2. Heat the liquid in a calorimeter with a known mass of water $m_{\text{water}}$ at initial temperature $T_{\text{initial}}$.
  3. Use a calibrated heating element (e.g., a nichrome wire) to supply a known amount of heat $Q$ (often measured via power × time).
  4. Record the final equilibrium temperature $T_{\text{final}}$.
  5. Apply energy conservation: $$Q + m_{\text{water}}c_{\text{water}}(T_{\text{initial}}-T_{\text{final}}) = m_{\text{liquid}}c_{\text{liquid}}(T_{\text{final}}-T_{\text{initial}})$$
  6. Rearrange to find $c_{\text{liquid}}$: $$c_{\text{liquid}}=\frac{Q + m_{\text{water}}c_{\text{water}}(T_{\text{initial}}-T_{\text{final}})}{m_{\text{liquid}}(T_{\text{final}}-T_{\text{initial}})}$$
Exam Tip: • If the heating element’s power $P$ (W) and time $t$ (s) are given, calculate $Q = Pt$. • Use the liquid’s density to convert volume to mass. • Keep the temperature change small to minimise heat loss to the calorimeter. • Double‑check units: $Q$ in J, masses in g, $\Delta T$ in °C.

Typical Specific Heat Values

Substance $c$ (J g⁻¹ °C⁻¹)
Water 4.18
Aluminium 0.900
Copper 0.385
Ethanol 2.44
Final Exam Reminder: • Always write the full equation with units. • Show all steps of algebraic manipulation. • Check that the final answer has the correct units (J g⁻¹ °C⁻¹). • Remember that heat lost by one component equals heat gained by the other (no loss to the environment in ideal problems). • Practice converting between joules, calories, and kilojoules if the question uses different units.

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