Question

if the energy absorbed by the ice is exactly equal to the energy lost by the water, what was the amount of energy needed to melt the ice? show your calculation.

Explanation:

To solve this, we need more information such as the mass of water, initial temperature of water, mass of ice, specific heat capacity of water, latent heat of fusion of ice, and the final temperature (if there's a temperature change). Since the problem statement is incomplete (missing values like mass, temperature, etc.), we can't perform the calculation yet. However, here's the general approach:

Step 1: Determine the energy lost by water

The energy lost by water can be calculated using the formula for heat transfer: \( Q = mc\Delta T \), where \( m \) is the mass of water, \( c \) is the specific heat capacity of water, and \( \Delta T \) is the change in temperature of water.

Step 2: Relate to energy absorbed by ice

Since the energy absorbed by ice (\( Q_{\text{ice}} \)) is equal to the energy lost by water (\( Q_{\text{water}} \)), and the energy absorbed by ice to melt is the latent heat of fusion (\( Q = mL_f \), where \( L_f \) is the latent heat of fusion of ice and \( m \) is the mass of ice), we can set \( mL_f = mc\Delta T \) (assuming all the energy lost by water goes into melting the ice, and there's no temperature change of ice other than phase change).

Answer:

To find the energy needed to melt the ice, we need additional information such as the mass of water, initial and final temperatures of water, mass of ice, and the latent heat of fusion of ice. Once we have these values, we can use the relationships between heat lost by water and heat absorbed by ice (for melting) to calculate the required energy.