Understanding the Problem
To determine the fraction of ice that melts when mixing equal masses of ice at -10°C with water at 60°C, we must consider the concepts of heat transfer and specific heat capacities.
Heat Transfer Principles
- Heat lost by warm water = Heat gained by ice
- Water will cool down to a certain temperature, while ice will absorb heat, causing it to melt.
Heat Required to Melt Ice
- To melt ice, we need to account for:
- The heat required to raise the temperature of ice from -10°C to 0°C (specific heat of ice).
- The heat required for phase change (melting) from ice to water (latent heat of fusion).
Calculating Heat Absorption
1. Heat gained by ice:
- Q1 = m * c_ice * ΔT (to reach 0°C)
- Q2 = m * L_f (latent heat of fusion)
2. Heat lost by water:
- Q_water = m * c_water * ΔT (from 60°C to equilibrium temperature)
Setting up the Equation
- The sum of heat gained by ice equals the heat lost by water:
- Q1 + Q2 = Q_water
Finding the Fraction of Ice Melted
- Let "x" be the mass of ice that melts.
- The total mass of ice is m, so the fraction that melts is x/m.
- By solving the heat exchange equation, we can find the value of x.
Conclusion
The fraction of ice that melts when mixing equal masses of ice at -10°C and water at 60°C can be calculated to reveal that a significant portion of ice will melt due to the heat transfer from the warmer water. The exact fraction depends on the specific heat capacities and latent heat values used in the calculations.