the heat of fusion water is 335J/g,the heat of vaporization of water is 2.26kJ/g, the specific heat of water is 4.184J/deg/g. how many grams of ice at 0 degrees could be converted to steam at 100 degrees C by 9,574J
To determine how many grams of ice could be converted to steam by 9,574J, we need to calculate the amount of energy required to convert the ice to water and then to steam.
First, let's calculate the heat required to convert the ice at 0 degrees Celsius to water at 0 degrees Celsius using the heat of fusion:
Heat required for phase change from ice to water = mass × heat of fusion
Heat required = mass × 335 J/g
Since we don't know the mass, we'll leave it as 'mass' for now.
Next, let's calculate the heat required to raise the temperature of the water from 0 degrees Celsius to 100 degrees Celsius using the specific heat:
Heat required to heat the water to 100 degrees Celsius = mass × specific heat × change in temperature
Heat required = mass × 4.184 J/°C/g × (100 - 0) °C
Again, we'll leave the mass as 'mass' for now.
Finally, let's calculate the heat required to convert the water at 100 degrees Celsius to steam at 100 degrees Celsius using the heat of vaporization:
Heat required for phase change from water to steam = mass × heat of vaporization
Heat required = mass × 2.26 kJ/g
Now, we can add all three heat values together to get the total heat required to convert the ice to steam:
9,574 J = (mass × 335 J/g) + (mass × 4.184 J/°C/g × 100 °C) + (mass × 2.26 kJ/g)
Now, let's solve for the mass:
9,574 J = (mass × 335 J/g) + (mass × 4.184 J/°C/g × 100 °C) + (mass × 2.26 kJ/g)
We can convert 2.26 kJ to J by multiplying it by 1000:
9,574 J = (mass × 335 J/g) + (mass × 4.184 J/°C/g × 100 °C) + (mass × 2.26 × 1000 J/g)
9,574 J = (mass × 335 J/g) + (mass × 4.184 J/°C/g × 100 °C) + (mass × 2,260 J/g)
Next, we can simplify the equation:
9,574 J = 335 mass + 418.4 mass + 2,260 mass
9,574 J = 3013.4 mass
Now, let's solve for mass:
mass = 9,574 J / 3013.4
mass ≈ 3.18 grams
Therefore, approximately 3.18 grams of ice at 0 degrees Celsius could be converted to steam at 100 degrees Celsius by 9,574 J of energy.
Let x = mass ice.
335*x = heat needed to melt ice.
4.184*100*x = heat needed to raise T of that ice from zero C to 100 C.
2260x = heat needed to vaporize the ice at 100 to steam at 100.
335x + (4.184*100*x) + 2260x = 9574 J. Solve for x.