12.8 kg of ice at 0 C is dropped into 3.3 kg of water at C. What fraction of the ice melts?
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To find the fraction of ice that melts, we need to determine the amount of energy transferred from the water to the ice, which will cause it to melt. This can be done using the concept of heat transfer and the specific heat capacities of ice and water.
The equation for heat transfer can be expressed as:
Q = m * c * ΔT
Where:
Q = Heat transfer
m = Mass
c = Specific heat capacity
ΔT = Change in temperature
First, let's calculate the amount of heat transferred from the water to the ice. Since the ice is initially at 0°C and will melt completely, its final temperature will also be 0°C. The water is initially at an unknown temperature, C, and its final temperature will also be 0°C after transferring heat to the ice.
For the water:
Q_water = m_water * c_water * ΔT_water
For the ice:
Q_ice = m_ice * c_ice * ΔT_ice
Since the final and initial temperatures are the same for both the water and the ice, the change in temperature will be 0:
ΔT_water = 0
ΔT_ice = 0
Therefore, the equations simplify to:
Q_water = m_water * c_water * 0
Q_ice = m_ice * c_ice * 0
As a result, the heat transferred from the water to the ice, Q_water, and the heat needed to melt the ice, Q_ice, are both equal to 0.
Therefore, no fraction of the ice melts.