How much heat is required to heat 0.1 g of
ice at −30 degrees C to steam at 100 degrees C
89
To determine the amount of heat required to heat 0.1 g of ice from -30 degrees Celsius to steam at 100 degrees Celsius, we need to consider the different stages of the phase changes and the specific heat capacities.
1. Heating ice from -30 degrees Celsius to 0 degrees Celsius:
The heat required can be calculated using the equation:
Q = m * c * ΔT
where
Q = heat energy
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
The specific heat capacity of ice is approximately 2.09 J/g°C.
So, for this step:
Q1 = 0.1 g * 2.09 J/g°C * (0 - (-30)°C)
Q1 = 0.1 g * 2.09 J/g°C * 30°C
Q1 = 6.27 J
2. Melting ice at 0 degrees Celsius:
The heat required for phase change can be calculated using the equation:
Q = m * ΔHf
where
Q = heat energy
m = mass of the substance
ΔHf = heat of fusion
The heat of fusion for ice is approximately 334 J/g.
So, for this step:
Q2 = 0.1 g * 334 J/g
Q2 = 33.4 J
3. Heating water from 0 degrees Celsius to 100 degrees Celsius:
The heat required can be calculated using the same equation as in step 1, but now using the specific heat capacity of water, which is approximately 4.18 J/g°C.
For this step:
Q3 = 0.1 g * 4.18 J/g°C * (100 - 0)°C
Q3 = 0.1 g * 4.18 J/g°C * 100°C
Q3 = 41.8 J
4. Boiling water at 100 degrees Celsius:
The heat required for the phase change can be calculated using the equation:
Q = m * ΔHv
where
Q = heat energy
m = mass of the substance
ΔHv = heat of vaporization
The heat of vaporization for water is approximately 2260 J/g.
So, for this step:
Q4 = 0.1 g * 2260 J/g
Q4 = 226 J
Now, we can calculate the total heat required:
Total heat = Q1 + Q2 + Q3 + Q4
Total heat = 6.27 J + 33.4 J + 41.8 J + 226 J
Total heat = 307.47 J
Therefore, approximately 307.47 J of heat is required to heat 0.1 g of ice at -30 degrees Celsius to steam at 100 degrees Celsius.
To calculate the heat required to heat ice at -30 degrees Celsius to steam at 100 degrees Celsius, we need to consider the different phases of water and their specific heat capacities. Here's how you can calculate it:
1. Determine the heat required to heat the ice from -30 degrees Celsius to 0 degrees Celsius:
The specific heat capacity of ice is 2.09 J/g·°C.
Therefore, the heat required can be calculated using the formula:
Heat = mass × specific heat capacity × change in temperature.
Heat = 0.1 g × 2.09 J/g·°C × (0 - (-30)°C).
2. Determine the heat required to melt the ice at 0 degrees Celsius:
The heat of fusion, which is the energy required to change a solid into a liquid at its melting point, is 334 J/g.
Therefore, the heat required to melt the ice can be calculated using the formula:
Heat = mass × heat of fusion.
Heat = 0.1 g × 334 J/g.
3. Determine the heat required to heat the water from 0 degrees Celsius to 100 degrees Celsius:
The specific heat capacity of water is approximately 4.18 J/g·°C.
Therefore, the heat required to heat the water is calculated using the formula:
Heat = mass × specific heat capacity × change in temperature.
Heat = 0.1 g × 4.18 J/g·°C × (100 - 0)°C.
4. Determine the heat required to vaporize the water at 100 degrees Celsius:
The heat of vaporization, which is the energy required to change a liquid into a gas at its boiling point, is approximately 2260 J/g.
Therefore, the heat required to vaporize the water can be calculated using the formula:
Heat = mass × heat of vaporization.
Heat = 0.1 g × 2260 J/g.
5. Finally, sum up all the heats calculated in steps 1 to 4 to get the total heat required for the transformation.
Total Heat = Heat Step 1 + Heat Step 2 + Heat Step 3 + Heat Step 4.
By plugging in the values and performing the calculations, you should be able to determine the total heat required.