calculate the energy required to heat 1.00L of ice at -50.0C to steam at 180.0C
q1 = heat to raise T of ice at -50C to zero C/
q1 = mass ice x specific heat ice x (50)
q2 = heat to melt the ice at zero to liquid at zero C.
q2 = mass ice x heat fusion.
q3 = heat to raise T of water at zero C to 100 C.
q3 = mass water x specific heat water x 100
q4 = heat to vaporize water at 100 C to steam at 100 C
q4 = mass water x heat vaporization
q5 = heat to raise T of steam at 100 C to steam at 180 C.
q5 = mass steam x specific heat steam x80
Total Q = q1 + q2+ q3 + q4 + q5
To calculate the energy required to heat the ice to steam, you'll need to consider several steps:
1. Calculate the energy required to raise the temperature of the ice from -50.0°C to 0.0°C.
2. Calculate the energy required to convert the ice at 0.0°C to water at 0.0°C.
3. Calculate the energy required to raise the temperature of the water from 0.0°C to 100.0°C.
4. Calculate the energy required to convert the water at 100.0°C to steam at 100.0°C.
5. Calculate the energy required to raise the temperature of the steam from 100.0°C to 180.0°C.
Let's go through each step:
1. To raise the temperature of the ice from -50.0°C to 0.0°C, you need to use the specific heat capacity equation:
q = m * c * ΔT
where:
q = energy (in Joules)
m = mass (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
The specific heat capacity of ice is approximately 2.09 J/g°C.
Assuming the density of ice is 0.92 g/mL and the volume is 1.00 L, the mass can be calculated as follows:
mass = density * volume
mass = 0.92 g/mL * 1.00 L * 1000 mL/1 L
mass = 920 g
With a change in temperature of 0.0°C - (-50.0°C) = 50.0°C, the energy required is:
q1 = 920 g * 2.09 J/g°C * 50.0°C
q1 = 96,680 J
2. To convert the ice at 0.0°C to water at 0.0°C, you need to calculate the energy using the following equation:
q = m * ΔH_fusion
where:
q = energy (in Joules)
m = mass (in grams)
ΔH_fusion = heat of fusion (in J/g)
The heat of fusion of ice is approximately 334 J/g.
The energy required is:
q2 = 920 g * 334 J/g
q2 = 307,280 J
3. To raise the temperature of the water from 0.0°C to 100.0°C, you need to calculate the energy:
q3 = m * c * ΔT
where:
q3 = energy (in Joules)
m = mass (in grams)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (in °C)
With a change in temperature of 100.0°C - 0.0°C = 100.0°C, the energy required is:
q3 = 920 g * 4.18 J/g°C * 100.0°C
q3 = 384,560 J
4. To convert the water at 100.0°C to steam at 100.0°C, you need to calculate the energy:
q4 = m * ΔH_vaporization
where:
q4 = energy (in Joules)
m = mass (in grams)
ΔH_vaporization = heat of vaporization (in J/g)
The heat of vaporization of water is approximately 2260 J/g.
The energy required is:
q4 = 920 g * 2260 J/g
q4 = 2,075,200 J
5. To raise the temperature of the steam from 100.0°C to 180.0°C, you need to calculate the energy:
q5 = m * c * ΔT
where:
q5 = energy (in Joules)
m = mass (in grams)
c = specific heat capacity of steam (2.03 J/g°C)
ΔT = change in temperature (in °C)
With a change in temperature of 180.0°C - 100.0°C = 80.0°C, the energy required is:
q5 = 920 g * 2.03 J/g°C * 80.0°C
q5 = 148,496 J
Finally, you can calculate the total energy required by summing up the energies from all the steps:
Total energy = q1 + q2 + q3 + q4 + q5
Total energy = 96,680 J + 307,280 J + 384,560 J + 2,075,200 J + 148,496 J
Total energy = 3,012,216 J