4. If you have 250 grams of ice at OC and want to melt it completely, how much heat energy is required given that the latent heat of fusion of water is \( 334 \mathrm{~kJ} / \mathrm{kg} \) ? Express your answer in kJ

To find the heat energy required to melt 250 grams of ice at 0°C, we can use the formula: \[ Q = m \times L_f \] where \(Q\) is the heat energy, \(m\) is the mass in kilograms, and \(L_f\) is the latent heat of fusion. First, we need to convert the mass from grams to kilograms: \[ 250 \, \text{g} = 0.250 \, \text{kg} \] Now, substituting the values into the formula: \[ Q = 0.250 \, \text{kg} \times 334 \, \text{kJ/kg} = 83.5 \, \text{kJ} \] Therefore, the heat energy required to melt the ice completely is \( \mathbf{83.5 \, kJ} \). --- Did you know that the process of melting ice is an endothermic reaction? This means that ice absorbs heat energy from its surroundings, leading to a temperature drop in its environment. This is why you sometimes feel chilly in a warm room if there's ice nearby! In real-world applications, understanding latent heat can help in designing climate control systems. For instance, using ice in HVAC systems can efficiently cool spaces because of its ability to absorb a significant amount of heat before it melts completely. This is quite an insightful method for energy conservation!