A perfectly insulated flask contains a sample of metal M at a temperature of -10 °C - AQA - A-Level Physics - Question 1 - 2020 - Paper 2

The energy transferred causes the atoms to vibrate more vigorously, which reduces the number of nearest atomic neighbors. This means the bonds that hold the atoms together start to break as they gain more energy, transitioning from a solid state towards a liquid state.

During the interval t_A to t_B, the total (or mean) kinetic energy remains constant while the total (or mean) potential energy increases due to the breaking of bonds.

During the time interval t_B to t_C, the motion of the atoms changes from being more fixed in position to becoming more fluid as they transition into the liquid state. The atoms gain energy, allowing for increased movement.

The specific heat capacity of M in the liquid state can be calculated using the formula:

$Q = mc heta$

Where:

• $Q$ is the heat supplied,
• $m$ is the mass,
• $c$ is the specific heat capacity,
• $\theta$ is the change in temperature.

Given the values:

• $m = 0.25 ext{ kg}$,
• $Q = 35 ext{ W} \times 60 \text{ s} = 2100 ext{ J}$,
• Change in temperature from -10 °C to 30 °C = 40 °C,

Thus:

$2100 = 0.25 \times c \times 40$

From which:

$c = \frac{2100}{0.25 \times 40} = 210 ext{ J kg}^{-1} \text{ °C}^{-1}$

Therefore, the specific heat capacity of M is 210 J kg⁻¹ °C⁻¹.

Based on the provided latent heats of fusion in Table 1, M corresponds to Gallium, which has a latent heat of fusion of 80 kJ kg⁻¹.