what is the number of grams of steam at 100 degrees C that will condense as 5g of ice at 0 degrees C melts?
To find the number of grams of steam that will condense, we can start by determining the amount of heat required to melt 5g of ice at 0 degrees Celsius.
The heat required to melt ice can be calculated using the heat of fusion of water, which is 334 J/g. Given that we have 5g of ice, we can find the total heat needed:
Heat = mass of ice * heat of fusion
Heat = 5g * 334 J/g
Heat = 1670 J
Now, in order for the steam to condense and release this amount of heat, it needs to cool from 100 degrees Celsius to 0 degrees Celsius and then change phase into water at 0 degrees Celsius.
To calculate the heat released during the cooling process, we can use the specific heat capacity of steam, which is approximately 2.03 J/g°C. The steam needs to cool by 100 degrees Celsius since its initial temperature is 100 degrees Celsius and its final temperature should be 0 degrees Celsius:
Heat released during cooling = mass of steam * specific heat capacity of steam * change in temperature
Heat released during cooling = mass of steam * 2.03 J/g°C * 100°C
Heat released during cooling = 203 J/g * mass of steam
Since the heat released during the cooling process must equal the heat required to melt the ice, we can set up the equation:
203 J/g * mass of steam = 1670 J
Simplifying the equation, we find:
mass of steam = 1670 J / 203 J/g
mass of steam ≈ 8.22 g
Therefore, approximately 8.22 grams of steam at 100 degrees Celsius will condense to provide the heat required to melt 5 grams of ice at 0 degrees Celsius.