How many grams of ice would be melted by the energy obtained as 16.2 of steam is condensed at 100 degrees celsius and cooled to 0 degrees celsius?
I would like to know how it's done step by step.
In calories.
heat lost by 16.2 g steam @ 100 C to condense to liquid is
q1 = mass x heat condensation.
q1 = 16.2 x 540 cal/g = ?
q2 = heat lost with H2O liquid moving from 100 C to 0C.
q2 = mass H2O x specific heat x (Tfinal-Tinitial) =
16.2 g x 1 cal/g*C x 100 C = ?
Total heat lost = q1 + q2 = ?
It takes 80 calories/g to melt ice so 80 cal/g x #g = q1 + q2
Solve for #g ice
To determine the number of grams of ice melted, we need to calculate the amount of heat released when the steam is condensed and cooled to 0 degrees Celsius and then convert this heat energy into the amount of ice melted.
Here are the steps to calculate it:
Step 1: Calculate the heat released when steam is condensed.
The heat released when steam is condensed can be calculated using the formula: Q = m * ΔHv, where Q is the heat energy, m is the mass of the substance, and ΔHv is the heat of vaporization.
First, we need to calculate the heat of vaporization (ΔHv) of steam. The heat of vaporization for water is 40.7 kJ/mol or 2.26 kJ/g. Therefore, ΔHv = 2.26 kJ/g.
Next, we need to calculate the mass of the steam that is condensed. You mentioned that 16.2 grams of steam is condensed. So, m = 16.2 grams.
Now we can calculate the heat released when steam is condensed:
Q = m * ΔHv
Q = 16.2 g * 2.26 kJ/g (Note: Make sure the units cancel out. Kilojoules need to be the final unit.)
Step 2: Calculate the heat released when the condensed water is cooled to 0 degrees Celsius.
The heat released can be calculated using the formula: Q = m * c * ΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Since the condensed water is cooled from 100 degrees Celsius to 0 degrees Celsius, ΔT = 100°C - 0°C = 100°C.
The specific heat capacity (c) of water is about 4.18 J/g°C.
Convert the heat released from kilojoules to joules:
Q = 16.2 g * 4.18 J/g°C * 100°C (Note: Make sure the units cancel out. Joules need to be the final unit.)
Step 3: Convert the total heat released into grams of ice melted.
To convert the heat energy released into grams of ice melted, we need to know the heat of fusion of ice. The heat of fusion for water is 333.55 kJ/kg or 333.55 J/g.
Divide the total heat released in joules by the heat of fusion of ice:
Q = Total heat released from the previous steps (in joules)
Mass of ice melted = Q / (333.55 J/g) (Note: Make sure the units cancel out. The final unit should be grams.)
Now, substitute the values and calculate:
Mass of ice melted = Q / (333.55 J/g)
Remember, the value of Q comes from Step 2.
By following these steps, you can calculate the grams of ice melted by the energy obtained when 16.2 grams of steam is condensed at 100 degrees Celsius and cooled to 0 degrees Celsius.
To calculate the grams of ice melted, we need to follow these steps:
Step 1: Calculate the energy required to condense the steam from 100 degrees Celsius to 100 degrees Celsius.
Step 2: Calculate the energy required to cool the condensed steam from 100 degrees Celsius to 0 degrees Celsius.
Step 3: Calculate the energy released when the cooled condensed steam is further cooled and becomes ice at 0 degrees Celsius.
Step 4: Convert the energy obtained in step 3 to grams of ice melted, assuming the enthalpy of fusion for water is 334 J/g.
Let's calculate each step step-by-step:
Step 1: Calculate energy to condense the steam
The heat of vaporization for water is 2260 J/g.
Energy = mass of steam * heat of vaporization
Energy = 16.2 g * 2260 J/g
Energy = 36612 J
Step 2: Calculate energy to cool the condensed steam
The specific heat capacity of steam is 2.03 J/g°C.
Energy = mass of steam * specific heat capacity * temperature change
Energy = 16.2 g * 2.03 J/g°C * (100°C - 100°C)
Energy = 0 J
Step 3: Calculate the energy released when the condensed steam is further cooled and becomes ice
The heat of fusion for water is 334 J/g.
Energy = mass of ice * heat of fusion
Energy = x g * 334 J/g
Energy = 334x J
Step 4: Convert the energy obtained in Step 3 to grams of ice melted
334x J = 36612 J
x = 36612 J / 334 J/g
x ≈ 109.57 g
Therefore, approximately 109.57 grams of ice would be melted by the energy obtained when 16.2 grams of steam is condensed at 100 degrees Celsius and cooled to 0 degrees Celsius.