A student sets up the apparatus shown in Fig. 10.1 to determine the specific heat capacity of aluminium. A cylindrical aluminium block of mass 1.0 kg has tw...

(a) Calculate the power of the heater from the joulemeter readings. [2]

Convert time to seconds: \(t = 5.0 \times 60 = 300\text{ s}\)

\(P = \frac{E}{t} = \frac{14\,400}{300}\) [1]

\(P = 48\text{ W}\) [1]

This confirms the heater's rated power of 48 W.

(b) Calculate the specific heat capacity of aluminium. [3]

Rearranging \(E = mc\Delta\theta\) to find \(c\):

\(c = \frac{E}{m\Delta\theta}\) [1]

The temperature rise is \(\Delta\theta = 38 - 22 = 16\text{ °C}\):

\(c = \frac{14\,400}{1.0 \times 16}\) [1]

\(c = 900\text{ J/(kg °C)}\) [1]

This means 900 J of energy is needed to raise the temperature of 1 kg of aluminium by 1 °C.

(c) Suggest two reasons why the student's value differs from the accepted value. [2]

1. Some energy is lost to the surroundings despite the insulation. This means the block absorbs less energy than the joulemeter records, making the measured temperature rise smaller than it should be. This gives a calculated value of \(c\) that is too high. [1]
2. The thermometer may not be in perfect thermal contact with the block (air gaps in the hole), so the recorded temperature rise is less than the actual temperature rise of the aluminium, again giving a value of \(c\) that is too high. [1]

(d) Explain the purpose of the oil in the thermometer hole. [1]

Oil fills the air gap between the thermometer bulb and the walls of the hole. Air is a poor conductor of heat, so without oil there would be slow heat transfer to the thermometer. Oil is a much better thermal conductor than air, ensuring the thermometer reads the true temperature of the block more quickly and accurately. [1]

(e) State one way the student could check the reliability of the result. [1]

Repeat the experiment (possibly using a different heating time or different starting temperature) and check whether the same value of \(c\) is obtained. Consistent results indicate the measurement is reliable. [1]