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)
Water4.18
Aluminium0.900
Copper0.385
Ethanol2.44

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.