An ice cube of volume 17.7 cm3 is initially at a temperature of -19.3°C. How much heat is required to convert this ice cube into steam?
Follow the following steps:
1. Calculate the ice block's mass from its volume and density.
2. Compute heat required to raise its temp. from -19.3 degC to 0 deg - Q1
3. Consider latent heat required to change the state from ice at 0 deg. to water at 0 deg. - Q2
3. Compute heat reqd. to raise water's temp. from 0 to 100 deg -Q3
4. Compute heat reqd. to change water at 100 deg to steam at 100 deg C. - Q4
Total heat required = Q1+Q2+Q3+Q4
Q=12,914.805 cal
To determine the amount of heat required to convert an ice cube into steam, we need to consider the different phases of matter and their respective heat transfer processes.
First, let's calculate the heat required to raise the temperature of the ice cube from -19.3°C to 0°C using the specific heat capacity formula:
Q1 = m * c * ΔT
Where:
Q1 is the heat required
m is the mass of the ice cube
c is the specific heat capacity of ice
ΔT is the change in temperature
The density of ice is approximately 0.92 g/cm^3, so the mass of the ice cube is:
m = density * volume
m = 0.92 g/cm^3 * 17.7 cm^3
Next, we need to convert the mass from grams to kilograms for the specific heat capacity and temperature calculations, so we divide by 1000:
m = (0.92 * 17.7) / 1000
Now, we know that the specific heat capacity of ice is approximately 2.09 J/g°C. The change in temperature (ΔT) is:
ΔT = 0°C - (-19.3°C)
After calculating ΔT, we can substitute the values into the equation and find Q1.
Next, we need to calculate the heat required for the phase change from solid to liquid. This is known as the heat of fusion. The heat of fusion for ice is approximately 334 J/g. We can use this formula:
Q2 = m * ΔHf
Where:
Q2 is the heat required for the phase change
m is the mass of the ice cube
ΔHf is the heat of fusion for ice
After calculating Q2, we move on to the final phase change from liquid water to steam. This requires calculating the heat of vaporization, which is the energy required for the phase change. The heat of vaporization for water is approximately 2260 J/g.
For the volume of ice, we need to convert it to mass using the density of ice:
m = density * volume
m = 0.92 g/cm^3 * 17.7 cm^3
Finally, we can calculate Q3 using the formula:
Q3 = m * ΔHv
Where:
Q3 is the heat required for the phase change
m is the mass of the water
ΔHv is the heat of vaporization for water
By adding Q1, Q2, and Q3, we will get the total heat required to convert the ice cube into steam.