An ice cube of volume 7.6 cm3 is initially at a temperature of -11.4°C. How much heat is required to convert this ice cube into steam?
435.5
To calculate the amount of heat required to convert the ice cube into steam, we need to consider the different phases of water and use the specific heat values associated with each phase.
The phase change for the ice cube involves three steps: heating the ice from its initial temperature (−11.4°C) to its melting point, melting the ice at 0°C, and then heating the resulting water from 0°C to the boiling point, and finally changing the water to steam.
Here are the steps to calculate the heat required:
Step 1: Heating the ice from -11.4°C to its melting point:
First, we need to calculate the heat required to raise the temperature of the ice cube from -11.4°C to 0°C. The specific heat capacity of ice is 2.09 J/g°C. To convert the volume of the ice cube to mass, we need to multiply it by the density of ice, which is 0.92 g/cm³.
Volume of ice cube = 7.6 cm³
Mass of ice = Volume × Density = 7.6 cm³ × 0.92 g/cm³ = 7.0 g
The heat required is calculated using the formula:
q = m × c × ΔT
where q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Using the data given:
ΔT = (0°C - (-11.4°C)) = 11.4°C
q1 = 7.0 g × 2.09 J/g°C × 11.4°C
q1 ≈ 171.93 J (rounded to two decimal places)
Step 2: Melting the ice at 0°C:
The heat required to change the phase of ice at 0°C to water at 0°C is calculated using the formula:
q = m × ΔHf
where q is the heat, m is the mass, and ΔHf is the heat of fusion or latent heat of fusion. For water, ΔHf is 334 J/g.
q2 = 7.0 g × 334 J/g
q2 ≈ 2338 J (rounded to the nearest whole number)
Step 3: Heating the water from 0°C to its boiling point:
To calculate the heat required to raise the temperature of water from 0°C to its boiling point, we need to use the specific heat capacity of water, which is 4.18 J/g°C.
Using the data given:
ΔT = (100°C - 0°C) = 100°C
q3 = 7.0 g × 4.18 J/g°C × 100°C
q3 ≈ 2926 J (rounded to the nearest whole number)
Step 4: Vaporization of water to steam:
The heat required to convert water at its boiling point (100°C) to steam at the same temperature is calculated using the formula:
q = m × ΔHv
where q is the heat, m is the mass, and ΔHv is the heat of vaporization or latent heat of vaporization for water, which is 2260 J/g.
q4 = 7.0 g × 2260 J/g
q4 ≈ 15820 J (rounded to the nearest whole number)
Finally, we can calculate the total heat required to convert the ice cube into steam by summing up the individual heat values:
Total heat required = q1 + q2 + q3 + q4
Total heat required ≈ 171.93 J + 2338 J + 2926 J + 15820 J
Total heat required ≈ 21155 J (rounded to the nearest whole number)
Therefore, approximately 21155 J of heat is required to convert the ice cube into steam.