Specific Heat Capacity and Practical Investigation

The Specific Heat Capacity Equation

The energy transferred when heating or cooling a substance is calculated using the following equation:

$$\Delta E = m \times c \times \Delta \theta$$

Where:

• $\Delta E$ = change in thermal energy, measured in Joules ($J$)
• $m$ = mass, measured in kilograms ($kg$)
• $c$ = specific heat capacity, measured in Joules per kilogram per degree Celsius ($J/kg^\circ\text{C}$)
• $\Delta \theta$ = change in temperature, measured in degrees Celsius ($^\circ\text{C}$) or Kelvin ($K$)

Note: A change in temperature of 1 °C is exactly the same magnitude as a change of 1 K, so OCR accepts either unit for temperature change.

Worked Example

A 2.5 kg block of copper is heated from 20 °C to 45 °C using 24,000 J of thermal energy. Calculate the specific heat capacity of the copper.

Step 1: Calculate the temperature change ($\Delta \theta$).

• $\Delta \theta = 45^\circ\text{C} - 20^\circ\text{C} = 25^\circ\text{C}$

Step 2: Rearrange the formula to make specific heat capacity ($c$) the subject.

• $c = \frac{\Delta E}{m \times \Delta \theta}$

Step 3: Substitute the values into the equation.

• $c = \frac{24000}{2.5 \times 25}$

Step 4: Calculate the final answer with units.

• $c = \frac{24000}{62.5} = 384\ J/kg^\circ\text{C}$

Investigating Specific Heat Capacity (PAG 5)

To determine the specific heat capacity of a material experimentally, you must carefully measure the energy supplied and the resulting temperature change.

1. Measure the mass of a metal block (e.g., aluminium or iron) using a digital balance.
2. Wrap the block tightly in insulation (such as cotton wool or bubble wrap) to reduce thermal energy transfer to the surroundings.
3. Place an immersion heater into the central hole of the block.
4. Place a thermometer into the smaller hole. Adding a few drops of oil or water into this hole improves thermal contact between the block and the thermometer.
5. Connect the heater in series with a power supply and use a joulemeter to measure the exact energy transferred. (Alternatively, use an ammeter and voltmeter, and calculate energy using $E = V \times I \times t$).
6. Record the initial temperature, switch on the heater, and start a stopwatch.
7. After a set time (e.g., 10 minutes), turn off the heater.
8. Wait for the temperature on the thermometer to reach its peak before recording the final temperature. This allows time for the heat to conduct fully through the block until thermal equilibrium is reached.

Accuracy and Data Analysis

• Systematic Errors: Experimental values for specific heat capacity are almost always higher than the true values. This is because thermal energy is inevitably lost to the environment or used to heat the immersion heater itself. The recorded energy ($\Delta E$) includes this "wasted" energy, making the calculated $c$ artificially high.
• Graphical Analysis: To find $c$ from a graph, OCR recommends plotting Energy ($J$) on the y-axis against Mass $\times$ Temperature Change ($$) on the x-axis.