The formation of condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 8.80 g of condensation forms on a glass containing water and 170 g of ice, how many grams will melt as a result? Assume no other heat transfer occurs. Use the heat of vaporization of water at 37°, as an approximation, in this problem.
(Lv=2256kJ/kg, or 539kcal/kg)
To calculate the grams of ice that will melt as a result of the condensation, we need to consider the heat transfer involved.
1. First, we need to find the heat released by the condensation of 8.80 g of water vapor. We can use the formula:
Q = m * Lv
Where Q is the heat released, m is the mass of the condensation, and Lv is the heat of vaporization of water.
Substituting the values, we have:
Q = 8.80 g * 2256 kJ/kg
2. Now, we have the heat released by the condensation. Since no other heat transfer occurs, this heat will be transferred to the ice, causing it to melt. We can use the formula:
Q = m * Lf
Where Q is the heat transferred, m is the mass of ice melted, and Lf is the heat of fusion of ice.
Substituting the known values and rearranging the equation to solve for m, we have:
m = Q / Lf
The heat of fusion of ice is approximately 334 kJ/kg.
Substituting the values we know:
m = (8.80 g * 2256 kJ/kg) / 334 kJ/kg
m ≈ 59.19 g
Therefore, approximately 59.19 grams of ice will melt as a result of the condensation.
To calculate the amount of ice that will melt due to the condensation forming on a glass of ice water, we need to determine the amount of heat transfer that occurs during the phase change.
The heat transferred during the phase change (melting or freezing) can be calculated using the formula:
Q = m * Lv
Where:
Q is the heat transferred (in Joules)
m is the mass of the substance undergoing the phase change (in kilograms)
Lv is the heat of vaporization (or heat of fusion) of the substance (in Joules per kilogram)
First, convert the given mass of condensation from grams to kilograms:
m_condensation = 8.80 g = 0.00880 kg
Next, use the heat of vaporization of water (Lv) to calculate the heat transferred during the phase change:
Q = m_condensation * Lv
Q = 0.00880 kg * 2256 kJ/kg
Q = 19.81 kJ
Since the heat transferred during the phase change is equal to the heat gained by the ice, we can assume that the ice will absorb this heat and melt.
To calculate the mass of ice that will melt, we need to use the heat of fusion (Lf) of water, which is the heat required to melt one kilogram of a substance at its melting point.
The heat transferred during the phase change can be calculated as:
Q = m_ice * Lf
Where:
Q is the heat transferred (in Joules)
m_ice is the mass of the ice (in kilograms)
Lf is the heat of fusion of water (in Joules per kilogram)
Based on the given information, we know:
Q = 19.81 kJ (from the previous calculation)
m_ice = 170 g = 0.170 kg
So, we can rearrange the formula to solve for the mass of ice:
m_ice = Q / Lf
m_ice = 19.81 kJ / Lf
Now we can substitute the heat of fusion of water at 37°, which is approximately 2256 kJ/kg or 539 kcal/kg:
m_ice = 19.81 kJ / 2256 kJ/kg
m_ice = 0.00880 kg
Therefore, approximately 0.00880 kg or 8.80 grams of ice will melt as a result of the condensation forming on the glass of ice water.