IGCSE Physics 0625 – Specific Heat Capacity
2.2.2 Specific Heat Capacity
Learning Objective
Describe experiments that can be used to determine the specific heat capacity of a solid and of a liquid.
Key Formula
The specific heat capacity \$c\$ of a material is defined by the relationship
\$c = \frac{Q}{m\Delta T}\$
where
\$Q\$ = heat energy transferred (J)
\$m\$ = mass of the substance (kg)
\$\Delta T\$ = temperature change (K or °C)
Experiment 1 – Determining the Specific Heat Capacity of a Solid (Calorimetric Method)
Apparatus
Item
Purpose
Calorimeter (insulated container with lid)
Minimise heat loss to surroundings
Known mass of water (\$m_{\text{w}}\$ )
Reference material with known \$c_{\text{w}} = 4186\ \text{J kg}^{-1}\text{K}^{-1}\$
Thermometer or temperature probe
Measure initial and final temperatures
Balance (to 0.1 g)
Determine masses of water and solid
Heated water bath
Raise the solid to a known temperature \$T_{\text{hot}}\$
Solid sample (e.g., metal block)
Object whose \$c\$ is to be found
Procedure (ordered steps)
Weigh the dry solid and record its mass \$m_{\text{s}}\$ .
Place a known mass of water \$m{\text{w}}\$ in the calorimeter and record its initial temperature \$T{\text{i}}\$ .
Heat the solid in a separate water bath until its temperature reaches \$T{\text{hot}}\$ (typically \$50–80^\circ\text{C}\$ ). Record \$T{\text{hot}}\$ .
Quickly transfer the hot solid into the calorimeter, close the lid, and stir gently.
Record the highest temperature reached by the water–solid mixture, \$T_{\text{f}}\$ .
Calculate the temperature changes:
\$\Delta T{\text{w}} = T {\text{f}} - T_{\text{i}}\$ (water)
\$\Delta T{\text{s}} = T {\text{hot}} - T_{\text{f}}\$ (solid)
Assuming negligible heat loss, set the heat lost by the solid equal to the heat gained by the water:\$m{\text{s}}c {\text{s}}\Delta T{\text{s}} = m {\text{w}}c{\text{w}}\Delta T {\text{w}}\$
Solve for \$c_{\text{s}}\$ :
\$c{\text{s}} = \frac{m {\text{w}}c{\text{w}}\Delta T {\text{w}}}{m{\text{s}}\Delta T {\text{s}}}\$
Sources of Error
Heat loss to the surroundings before the lid is closed.
Incomplete thermal equilibrium between solid and water.
Inaccurate temperature readings (thermometer lag).
Water evaporating during the experiment.
Suggested diagram: Schematic of the calorimeter setup with the solid being dropped in, showing the thermometer and lid.
Experiment 2 – Determining the Specific Heat Capacity of a Liquid (Method of Mixing)
Apparatus
Item
Purpose
Two beakers (insulated)
Contain hot and cold liquids separately
Thermometer or temperature probe
Measure temperatures before and after mixing
Balance
Measure masses of the two liquids
Hot water bath
Heat the liquid whose \$c\$ is to be found
Cold water (or ice water)
Reference liquid with known \$c_{\text{w}}\$
Procedure
Measure and record the mass \$m{\text{x}}\$ of the liquid under test (e.g., oil) and heat it to a known temperature \$T{\text{x}}\$ .
Measure and record the mass \$m{\text{w}}\$ of cold water at temperature \$T{\text{w}}\$ (usually \$10–20^\circ\text{C}\$ ).
Quickly pour the hot liquid into the water, stir gently, and record the equilibrium temperature \$T_{\text{f}}\$ .
Assuming no heat loss, set heat lost by the hot liquid equal to heat gained by the water:\$m{\text{x}}c {\text{x}}(T{\text{x}}-T {\text{f}})=m{\text{w}}c {\text{w}}(T{\text{f}}-T {\text{w}})\$
Solve for \$c_{\text{x}}\$ :
\$c{\text{x}} = \frac{m {\text{w}}c{\text{w}}(T {\text{f}}-T{\text{w}})}{m {\text{x}}(T{\text{x}}-T {\text{f}})}\$
Sources of Error
Heat exchange with the environment during transfer.
Incomplete mixing leading to temperature gradients.
Inaccurate mass measurements if liquid adheres to containers.
Assumption that the specific heat of water remains constant over the temperature range.
Suggested diagram: Two beakers, one with hot liquid X and one with cold water, showing mixing and temperature probe.
Summary
Both experiments rely on the principle of conservation of energy: the heat lost by a hotter substance equals the heat gained by a cooler one, provided heat loss to the surroundings is negligible. By measuring masses, initial and final temperatures, and using the known specific heat capacity of water, the unknown specific heat capacity of a solid or liquid can be calculated using the derived algebraic expressions.