How much heat must be added to change 10g of ice at -10°C to steam at 110°C?
To determine the amount of heat required, we need to consider the different phases of matter involved and their corresponding specific heat capacities and heat of fusion/vaporization.
Let's break down the steps involved:
1. Heating the ice from -10°C to 0°C:
The ice is initially at -10°C, and we need to heat it until it reaches the melting point at 0°C.
The specific heat capacity of ice is approximately 2.09 J/g °C.
The equation to calculate the heat required is: Q = m * c * ΔT
where Q is the heat (in joules), m is the mass (in grams), c is the specific heat capacity (in J/g °C), and ΔT is the change in temperature (in °C).
Substituting the values: Q1 = 10g * 2.09 J/g °C * (0°C - (-10°C))
2. Melting the ice at 0°C:
Once the ice reaches 0°C, we need to calculate the heat required for the phase change from solid to liquid (ice to water) using the heat of fusion.
The heat of fusion for water is approximately 334 J/g.
The equation to calculate the heat required is: Q = m * ΔHf
where Q is the heat (in joules), m is the mass (in grams), and ΔHf is the heat of fusion (in J/g).
Substituting the values: Q2 = 10g * 334 J/g
3. Heating the water from 0°C to 100°C:
Once all the ice has melted, we need to heat the water from 0°C to its boiling point at 100°C.
The specific heat capacity of water is approximately 4.18 J/g °C.
The equation to calculate the heat required is: Q = m * c * ΔT
Substituting the values: Q3 = 10g * 4.18 J/g °C * (100°C - 0°C)
4. Vaporizing the water at 100°C:
After reaching 100°C, we need to calculate the heat required for the phase change from liquid to gas (water to steam) using the heat of vaporization.
The heat of vaporization for water is approximately 2260 J/g.
The equation to calculate the heat required is: Q = m * ΔHv
Substituting the values: Q4 = 10g * 2260 J/g
5. Heating the steam from 100°C to 110°C:
Finally, we need to heat the steam from 100°C to 110°C.
The specific heat capacity of steam is approximately 2.03 J/g °C.
The equation to calculate the heat required is: Q = m * c * ΔT
Substituting the values: Q5 = 10g * 2.03 J/g °C * (110°C - 100°C)
Now, to find the total heat required, we sum up all the individual Q values:
Total heat required = Q1 + Q2 + Q3 + Q4 + Q5
Just perform the calculations using the provided formulas and values to determine the total amount of heat required.