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 reduces the number of nearest atomic neighbours, allowing atoms to move their center of vibration. This can also be expressed as breaking some of the atomic bonds, transitioning the material from a crystalline to an amorphous state.

During the time interval tA to tB, the total or mean kinetic energy remains constant, while the total or mean potential energy increases.

During the time interval tB to tC, the mean speed of the atoms increases as they gain energy, leading to greater kinetic energy among the particles.

Using the formula for specific heat capacity, we have:

$Q = mc\Delta T$

Given: mass $m = 0.25 \, kg$, heat supplied $Q = 35 \, W imes (t_2 - t_1)$ for $t_{AB} = 14.8 \text{ minutes} - 3.5 \text{ minutes} = 11.3 \text{ minutes}$. Therefore, total heat supplied is:

$Q = 35 \times (11.3 \times 60) = 239.1 \ kJ$

Calculating for the specific heat capacity:

$c = \frac{Q}{m\Delta T}$

Let the change in temperature be $\Delta T = 28 - (-10) = 38 \, °C$,

So,

$c = \frac{239.1 \, kJ}{0.25 \, kg \times 38 \, °C} = 250.18 \, \frac{kJ}{kg \, K}$

Thus, the specific heat capacity of M in the liquid state is approximately 250.2 kJ kg⁻¹ K⁻¹.

Based on the latent heats of fusion provided in Table 1, the element M can be identified as Gallium, which has a latent heat of fusion of 80 kJ kg⁻¹.