Show the equation that 100g of 100C steam will completely melt 800g of 0C ice.
To determine the equation that represents the process of melting ice with steam, we need to consider the energy exchange that occurs during the process.
First, let's calculate the heat required to raise the temperature of 100g of steam at 100°C to water at 100°C using the formula:
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) which is approximately 2.03 J/g°C for water,
and ΔT is the change in temperature.
Using the equation, the heat required to raise the temperature of 100g of steam from 100°C to 100°C (no temperature change) is:
q1 = 100g * 2.03 J/g°C * (100°C - 100°C) = 0 Joules
Since there is no temperature change, no heat is required.
Next, let's calculate the heat required to convert 100g of steam at 100°C to water at 100°C using the formula:
q = m * ΔHvap
Where:
q is the heat (in Joules),
m is the mass (in grams),
ΔHvap is the enthalpy of vaporization (in J/g) which is approximately 2257 J/g for water.
Using the equation, the heat required to convert 100g of steam at 100°C to water at 100°C is:
q2 = 100g * 2257 J/g = 225,700 Joules
Now, let's calculate the heat required to lower the temperature of 800g of ice at 0°C to water at 0°C:
q3 = m * c * ΔT
Using the equation, the heat required to lower the temperature of 800g of ice from 0°C to 0°C (no temperature change) is:
q3 = 800g * 2.09 J/g°C * (0°C - 0°C) = 0 Joules
Since there is no temperature change, no heat is required.
Finally, let's calculate the heat required to melt 800g of ice at 0°C to water at 0°C using the formula:
q = m * ΔHfusion
Where:
q is the heat (in Joules),
m is the mass (in grams),
ΔHfusion is the enthalpy of fusion (in J/g) which is approximately 333.55 J/g for water.
Using the equation, the heat required to melt 800g of ice at 0°C to water at 0°C is:
q4 = 800g * 333.55 J/g = 266,840 Joules
Now, to find the total heat exchanged, we sum up all the heat values:
Total heat exchanged = q1 (no temperature change of steam) + q2 (conversion of steam to water) + q3 (no temperature change of ice) + q4 (conversion of ice to water)
Total heat exchanged = 0 Joules + 225,700 Joules + 0 Joules + 266,840 Joules
Total heat exchanged = 492,540 Joules
Therefore, the equation that represents the process of completely melting 800g of 0°C ice with 100g of 100°C steam is:
100g steam + 492,540 J => 800g ice