How many kilojoules are required to melt 15g of ice at 0 degree celsius, and raise the temperature of the liquid that forms to 85 degree celsius?
Well, melting ice can be quite a chilling experience, but don't worry, I'm here to keep things cool. When it comes to calculating the energy needed, we can break it down into two parts: melting the ice and then heating the resulting liquid.
To melt 15g of ice at 0 degrees Celsius, we need to use the heat of fusion formula, which tells us that it takes 334 joules per gram to melt ice. So, for 15g, that would be 15g x 334 J/g = 5010 joules.
Now, once all the ice is melted, we need to heat the liquid up from 0 degrees Celsius to 85 degrees Celsius. To calculate that, we can use the specific heat capacity of water, which is 4.18 joules per gram-degree Celsius. So, for 15g of water, it would take 15g x 85 degrees Celsius x 4.18 J/g°C = 5358.75 joules.
Adding these two values together, we get a grand total of 5010 joules + 5358.75 joules = 10368.75 joules, or approximately 10.4 kilojoules.
So, to answer your question, it would take around 10.4 kilojoules to melt 15g of ice at 0 degrees Celsius and raise the temperature of the resulting liquid to 85 degrees Celsius. We wouldn't want things to get too heated now, would we?
To calculate the total number of kilojoules required to melt the ice and raise the temperature of the resulting liquid, we need to consider two separate processes:
1. Melting the ice:
The energy required to melt a substance can be calculated using the formula:
Q = m * ΔHf
where:
Q is the heat energy required (in joules)
m is the mass of the substance (in grams)
ΔHf is the heat of fusion, which is the energy required to change a substance from a solid to a liquid (in joules per gram)
In the case of ice, the heat of fusion is approximately 334 J/g.
Using this formula, we can calculate the energy required to melt the ice:
Q1 = 15 g * 334 J/g
To convert this to kilojoules, we divide by 1000:
Q1 = (15 g * 334 J/g) / 1000 = 5.01 kJ
Therefore, approximately 5.01 kilojoules of energy are required to melt 15 grams of ice at 0 degrees Celsius.
2. Raising the temperature of the liquid:
The energy required to raise the temperature of a substance can be calculated using the formula:
Q = m * c * ΔT
where:
Q is the heat energy required (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in joules per gram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
For water, the specific heat capacity is approximately 4.18 J/g°C.
Using this formula, we can calculate the energy required to raise the temperature of the liquid:
Q2 = 15 g * 4.18 J/g°C * (85°C - 0°C)
To convert this to kilojoules, we divide by 1000:
Q2 = (15 g * 4.18 J/g°C * 85°C) / 1000 = 5.34 kJ
Therefore, approximately 5.34 kilojoules of energy are required to raise the temperature of the liquid that forms from 0 degrees Celsius to 85 degrees Celsius.
To find the total energy required, we add the two values:
Total energy = Q1 + Q2 = 5.01 kJ + 5.34 kJ = 10.35 kJ
Therefore, approximately 10.35 kilojoules of energy are required to melt 15 grams of ice at 0 degrees Celsius and raise the temperature of the resulting liquid to 85 degrees Celsius.
To calculate the total amount of energy required, we need to consider two separate processes: melting the ice and then raising the temperature of the resulting liquid.
First, let's calculate the energy required to melt the ice. This can be done using the equation:
Q = m * ΔHf
Where:
Q = amount of energy (in kilojoules)
m = mass of the substance (in grams)
ΔHf = heat of fusion (for ice, this value is approximately 334 J/g)
Converting the mass to grams, we have m = 15 g.
Q = 15 g * 334 J/g = 5010 J
To convert from joules to kilojoules, we divide by 1000:
Q = 5010 J / 1000 = 5.01 kJ
So, the energy required to melt 15g of ice at 0 degrees Celsius is approximately 5.01 kilojoules.
Next, for raising the temperature of the liquid from 0 degrees Celsius to 85 degrees Celsius, we use the equation:
Q = m * c * ΔT
Where:
Q = amount of energy (in kilojoules)
m = mass of the substance (in grams)
c = specific heat capacity (for water, this value is approximately 4.184 J/g °C)
ΔT = change in temperature (in degrees Celsius)
Converting the mass to grams, we have m = 15 g.
ΔT = 85 °C - 0 °C = 85 °C
Q = 15 g * 4.184 J/g °C * 85 °C = 5358 J
Converting from joules to kilojoules:
Q = 5358 J / 1000 = 5.358 kJ
So, the energy required to raise the temperature of the liquid from 0 degrees Celsius to 85 degrees Celsius is approximately 5.358 kilojoules.
To find the total energy required, we add the energy for melting the ice and the energy for heating the liquid:
Total energy = Energy for melting + Energy for heating
Total energy ≈ 5.01 kJ + 5.358 kJ ≈ 10.368 kJ
Therefore, approximately 10.368 kilojoules of energy are required to melt 15g of ice at 0 degrees Celsius and raise the temperature of the resulting liquid to 85 degrees Celsius.
q1 = heat needed to change phase of ice from solid at zero C to liquid at zero C is
q1 = mass ice x heat fusion = ?
q2 = heat needed to raise the T from zero C to 85 C.
q2 = mass H2O x specific heat H2O x (Tfinal-Tinitial) = ?
q total = q1 + q2