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 determine how many grams of ice will melt as a result of condensation, we need to calculate the amount of heat transferred from the condensation to the ice.
The heat transfer can be calculated using the formula:
Q = m * Lv
Where:
Q is the amount of heat transferred in joules (J),
m is the mass of the condensation in grams (g), and
Lv is the heat of vaporization of water.
First, we need to convert the given heat of vaporization from kilojoules per kilogram (kJ/kg) to joules per gram (J/g). Dividing the heat of vaporization by 1000 will give us the conversion factor:
Lv = 2256 kJ/kg = 2256 J/g
Now, let's plug in the values into the equation:
Q = 8.80 g * 2256 J/g = 19,849.6 J
Next, we need to calculate the amount of ice that will melt using the heat of fusion of ice, which is the amount of heat required to convert a gram of ice to water at the same temperature. The heat of fusion of ice is equal to 334 J/g.
Therefore, the mass of ice that will melt can be calculated as:
m_ice = Q / heat of fusion
m_ice = 19,849.6 J / 334 J/g = 59.34 g
Therefore, approximately 59.34 grams of ice will melt as a result of the condensation forming on the glass containing water and ice.