A student performed a single experiment to (a) verify Joule's law, and (b) determine the specific heat capacity of olive oil - Leaving Cert Physics - Question 5 - 2022

The mass of olive oil was determined by using a calorimeter. First, the mass of the calorimeter when empty was measured. Then, the calorimeter was filled to a known level with room-temperature olive oil, and the mass of the full calorimeter was re-measured. The mass of the olive oil can then be calculated by subtracting the mass of the empty calorimeter from the mass of the full calorimeter.

To verify Joule's law, plot a graph of the power (P) against the temperature rise (Δθ).

• The x-axis will represent the temperature change (Δθ) in °C, calculated as θ - 17.0°C, while the y-axis will represent the calculated power (P) in Watts, determined using the formula:

$P = I^2 R$

where R is the resistance of the coil (8.5 Ω). Ensure that the graph is clearly labelled with appropriate axes.

To find the slope of the graph, use the formula for the slope, which is:

$m = \frac{\Delta P}{\Delta (\Delta \theta)}$

You will need to calculate the change in power and the change in temperature. For instance, using the data:

• From the recorded values, choose two points on the line of best fit and calculate the difference in their P and Δθ values.

This gives the slope which can then be reported.

The specific heat capacity (c) of olive oil can be calculated using the formula:

$c = \frac{m c_0}{P R T}$

Where:

• m = mass of olive oil (0.35 kg)
• c_0 = 4.18 J/g°C (specific heat capacity of water, as a proxy if needed)
• P = average power calculated from the slope;
• R = resistance of the coil (8.5 Ω);
• T = time in seconds (3 minutes = 180 seconds).

Plug in the values to get:

$c = \frac{(0.35)(4.18)}{8.5 * 180} = 1954 \text{ J kg}^{-1} ext{ K}^{-1}$