What is the amount of heat required to raise th... - JAMB Physics 2023 Question

To calculate the total heat required, we need to consider the following:

1. Heating the ice from \(-10^oC\) to \(0^oC\) using the specific heat capacity of ice.
2. Melting the ice at \(0^oC\) to water using the specific latent heat of fusion.
3. Heating the water from \(0^oC\) to \(10^oC\) using the specific heat capacity of water.

Let's calculate each part:

1. Heating ice from \(-10^oC\) to \(0^oC\):
   \[ Q_1 = mc\Delta T \]
   \[ Q_1 = 0.02 \, \text{kg} \times 2100 \, \text{J/kg} \, ^\circ\text{C} \times (0 - (-10)) \, ^\circ\text{C} \]
   \[ Q_1 = 0.02 \times 2100 \times 10 \]
   \[ Q_1 = 420 \, \text{J} \]

2. Melting the ice at \(0^oC\) to water:
   \[ Q_2 = mL_f \]
   \[ Q_2 = 0.02 \, \text{kg} \times 3.34 \times 10^5 \, \text{J/kg} \]
   \[ Q_2 = 6680 \, \text{J} \]

3. Heating water from \(0^oC\) to \(10^oC\):
   \[ Q_3 = mc\Delta T \]
   \[ Q_3 = 0.02 \, \text{kg} \times 4200 \, \text{J/kg} \, ^\circ\text{C} \times (10 - 0) \, ^\circ\text{C} \]
   \[ Q_3 = 0.02 \times 4200 \times 10 \]
   \[ Q_3 = 840 \, \text{J} \]

Now, add up the three quantities to get the total heat required:
\[ \text{Total heat} = Q_1 + Q_2 + Q_3 = 420 + 6680 + 840 = 7940 \, \text{J} \]

Therefore, the correct answer is: 7940 J