To calculate the energy needed to convert ice to water, we need to consider two different processes: raising the temperature of the ice from -14.6°C to 0°C, and then melting the ice at 0°C to water at 25.8°C. Let's break down the calculation step by step.
First, let's calculate the energy needed to raise the temperature of the ice from -14.6°C to 0°C. We'll use the formula:
q = mcΔT
where:
q = energy (in Joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
Given values:
m = 104 g
c = 2.01 J/g°C
ΔT = (0°C - (-14.6°C)) = 14.6°C
Calculating q:
q = (104 g) x (2.01 J/g°C) x (14.6°C)
q = 3013.84 J
So, the energy needed to raise the temperature of the ice from -14.6°C to 0°C is 3013.84 J.
Next, let's calculate the energy needed to melt the ice at 0°C to water at 25.8°C. The energy required for melting (also known as heat of fusion) can be calculated using the formula:
q = m ΔHf
where:
q = energy (in Joules)
m = mass of the substance (in grams)
ΔHf = heat of fusion (in J/g)
The heat of fusion for water is 334 J/g.
Given values:
m = 104 g
ΔHf = 334 J/g
Calculating q:
q = (104 g) x (334 J/g)
q = 34736 J
So, the energy needed to melt the ice at 0°C to water at 25.8°C is 34736 J.
Finally, we add the two energy values together to obtain the total energy required:
Total energy = energy to raise temperature + energy to melt ice
Total energy = 3013.84 J + 34736 J
Total energy ≈ 37749 J
Therefore, approximately 37749 Joules of energy are needed to convert 104 g of ice at -14.6°C to water at 25.8°C.