Calculate how many joules of (total) heat energy are needed to convert the ice at -25.0 *C to steam at 100.0 *C?
How much mass of ice is there?
You need the specific heats of ice and of water; the heat of vaporization, and the heat of fusion to answer this question.
C,ice = 0.5 Cal/g C
C,water = 1.0 Cal/g C
H,fusion = 80 Cal/g
H,vaporization = 540 Cal/g
For Joules, multiply each by 4.184 J/Cal
Total heat energy required =
M*[C,ice*25C + H,fusion, + C,water * 100C + H.vaporization)
the heat required to convert 2 kg ice of -5
OC to 100 OC water.
To calculate the total heat energy needed to convert the ice at -25.0 °C to steam at 100.0 °C, we need to consider the heat energy required for the following three phases:
1. Heating the ice from -25.0 °C to 0.0 °C
2. Melting the ice at 0.0 °C to liquid water at 0.0 °C
3. Heating the liquid water from 0.0 °C to 100.0 °C
4. Evaporating the water at 100.0 °C to steam at 100.0 °C
Now, let's calculate the amount of heat energy required in each step:
1. Heating the ice:
To heat the ice from -25.0 °C to 0.0 °C, we need to calculate the heat energy using the formula:
Q = m * C * ΔT
where:
Q = heat energy (in Joules)
m = mass of the ice (in grams)
C = specific heat capacity of ice (2.09 J/g°C)
ΔT = change in temperature (0.0 °C - (-25.0 °C) = 25.0 °C)
Assuming the mass of the ice is 1g (as an example):
Q1 = 1g * 2.09 J/g°C * 25.0 °C
Q1 = 52.25 Joules
2. Melting the ice:
To melt the ice, we need to calculate the heat energy using the formula:
Q = m * ΔHfus
where:
Q = heat energy (in Joules)
m = mass of the ice (in grams)
ΔHfus = heat of fusion of ice (334 J/g)
Assuming the mass of the ice is 1g (as an example):
Q2 = 1g * 334 J/g
Q2 = 334 Joules
3. Heating the liquid water:
To heat the liquid water from 0.0 °C to 100.0 °C, we need to calculate the heat energy using the formula:
Q = m * C * ΔT
where:
Q = heat energy (in Joules)
m = mass of the liquid water (in grams)
C = specific heat capacity of liquid water (4.18 J/g°C)
ΔT = change in temperature (100.0 °C - 0.0 °C = 100.0 °C)
Assuming the mass of the liquid water is 1g (as an example):
Q3 = 1g * 4.18 J/g°C * 100.0 °C
Q3 = 418 Joules
4. Evaporating the water:
To convert water into steam, we need to calculate the heat energy using the formula:
Q = m * ΔHvap
where:
Q = heat energy (in Joules)
m = mass of the liquid water (in grams)
ΔHvap = heat of vaporization of water (2260 J/g)
Assuming the mass of the liquid water is 1g (as an example):
Q4 = 1g * 2260 J/g
Q4 = 2260 Joules
Now, let's calculate the total heat energy required:
Total energy = Q1 + Q2 + Q3 + Q4
Total energy = 52.25 Joules + 334 Joules + 418 Joules + 2260 Joules
Total energy = 3064.25 Joules
Therefore, approximately 3064.25 Joules of heat energy are needed to convert the ice at -25.0 °C to steam at 100.0 °C.
To calculate the amount of energy required to convert the ice at -25.0 *C to steam at 100.0 *C, we need to consider the energy required for three different phases: heating the ice to 0 *C, melting the ice at 0 *C, and then heating the resulting water from 0 *C to 100.0 *C.
Let's break down the calculations step by step:
1. Heating the ice from -25.0 *C to 0 *C:
The specific heat capacity of ice is 2.09 J/g * *C (joules/gram/degree Celsius).
The formula to calculate the energy required is:
Energy = mass * specific heat capacity * change in temperature
For example, let's assume we have 100 grams of ice:
Energy = 100 g * 2.09 J/g * *C * (0 - (-25.0)) *C
2. Melting the ice at 0 *C:
The heat of fusion for ice at 0 *C is 334 J/g.
The formula to calculate the energy required is:
Energy = mass * heat of fusion
Using the same example of 100 grams of ice:
Energy = 100 g * 334 J/g
3. Heating the resulting water from 0 *C to 100.0 *C:
The specific heat capacity of water is 4.18 J/g * *C (joules/gram/degree Celsius).
The formula to calculate the energy required is:
Energy = mass * specific heat capacity * change in temperature
Using the same example of 100 grams of water:
Energy = 100 g * 4.18 J/g * *C * (100.0 - 0) *C
Now, we can add up the energies calculated for each step to get the total energy required to convert the ice to steam.
Please note that the specific heat capacities and heat of fusion values used in the calculations are approximate. Different sources may vary slightly, so always refer to the most accurate and appropriate values for your specific context.