You have 325 g of water at 18C. What is the most ice (at 0C) that you could put into this water and have it all melt?
To determine the maximum amount of ice that can be added to the water and melt completely, we need to consider the concept of heat transfer.
1. Calculate the heat absorbed by the water:
The formula for calculating heat transfer is:
Q = m * c * ΔT
where:
Q is the heat absorbed or released,
m is the mass of the substance,
c is the specific heat capacity of the substance,
ΔT is the change in temperature.
For water, the specific heat capacity is approximately 4.18 J/g°C.
Q = (mass of water) * (specific heat capacity of water) * (change in temperature)
Q = (325 g) * (4.18 J/g°C) * (final temperature - initial temperature)
As the water is initially at 18°C but we want it to melt all the ice at 0°C, the change in temperature is:
ΔT = 0°C - 18°C = -18°C
Q = (325 g) * (4.18 J/g°C) * (-18°C)
2. Calculate the heat released by the ice:
To melt ice into water, heat needs to be transferred from the water to the ice. The heat released by the ice can be calculated using the formula:
Q = m * L_f
where:
Q is the heat absorbed or released,
m is the mass of the substance,
L_f is the heat of fusion (latent heat) of the substance.
For ice, the heat of fusion is approximately 334 J/g.
Q = (mass of ice) * (heat of fusion of ice)
Rearranging this equation, we can solve for the mass of ice:
(mass of ice) = Q / (heat of fusion of ice)
Since we want all the water to melt, the heat released by the ice should be equal to the heat absorbed by the water.
(mass of ice) = Q / (heat of fusion of ice)
3. Calculate the mass of ice:
Substituting the values into the equation:
(mass of ice) = (325 g * 4.18 J/g°C * (-18°C)) / (334 J/g)
Calculate the mass of ice to find the maximum amount that can be added to the water and melt completely.
By plugging in the given values into the equation, we can determine that the maximum amount of ice that can be added to the water and melt completely is approximately 209.28 grams.