How many kilojoules of energy are needed to convert 104 g of ice at -14.6 to water at 25.8°C? (The specific heat of ice at -14.6 is 2.01 J/g°C.)
you can use the equation:
c=heat transferred/mass X change in temperature
c=2.01J/gC
mass= 104g
chaneg in temp = 40.4C
2.01= x/ 104g x 40.4C
x=8445.21J then divide that number by 1000 to get kJ the answer is 8.44kJ
you can check my calculations but that should be the correct equation.
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.