A student placed a metal block of mass 220g in boiling water at 100°C for several minutes - Edexcel - A-Level Physics - Question 12 - 2023 - Paper 2

The total energy gained by the water and glass can be calculated as:

$Q_{water} + Q_{glass} = m_{water}c_{water}\Delta T_{water} + m_{glass}c_{glass}\Delta T_{glass}$

For water:

• $m_{water} = 0.3$ kg,
• $c_{water} = 4200 \text{ J/kg K}$,
• $\Delta T_{water} = 23°C - 19°C = 4 K$.

Thus, $Q_{water} = 0.3 \text{ kg} \times 4200 \text{ J/kg K} \times 4 K = 5040 \text{ J}$

For glass:

• $m_{glass} = 0.05$ kg,
• $c_{glass} = 840 \text{ J/kg K}$,
• $\Delta T_{glass} = 4 K$.

Thus, $Q_{glass} = 0.05 \text{ kg} \times 840 \text{ J/kg K} \times 4 K = 168 \text{ J}$

The total energy gained is:

$Q_{total} = Q_{water} + Q_{glass} = 5040 \text{ J} + 168 \text{ J} = 5208 \text{ J}$

Setting the energy lost equal to the energy gained:

$0.22 \text{ kg} \times c \times 77 K = 5208 \text{ J}$

Solving for $c$ gives:

$c = \frac{5208 \text{ J}}{0.22 \text{ kg} \times 77 K} = 309.2 \text{ J/kg K}$

Since 309.2 J/kg K is not equal to the specific heat capacities of copper (390 J/kg K) or tin (230 J/kg K), we conclude the metal block is not made of either copper or tin, as the specific heat capacity of the block does not match either material.