5g ice at 0 degree Celsius is mixed with 5g steam at 100 degree Celsiu...
Problem:
5g ice at 0 degree Celsius is mixed with 5g steam at 100 degree Celsius. What is the final temperature of the mixture?
Solution:
Step 1: Calculate heat absorbed by ice to reach its melting point
Heat absorbed by ice = mass of ice x specific heat of ice x change in temperature
Heat absorbed by ice = 5g x 2.09 J/g°C x (0°C - (-0.00°C))
Heat absorbed by ice = 10.45 J
Step 2: Calculate heat absorbed by ice to melt it
Heat absorbed by ice to melt = mass of ice x heat of fusion of ice
Heat absorbed by ice to melt = 5g x 334 J/g
Heat absorbed by ice to melt = 1670 J
Step 3: Calculate heat absorbed by water to reach 100 degree Celsius
Heat absorbed by water = mass of water x specific heat of water x change in temperature
Heat absorbed by water = 5g x 4.18 J/g°C x (100°C - 0°C)
Heat absorbed by water = 2090 J
Step 4: Calculate heat absorbed by steam to condense it
Heat absorbed by steam to condense = mass of steam x heat of vaporization of water
Heat absorbed by steam to condense = 5g x 2260 J/g
Heat absorbed by steam to condense = 11300 J
Step 5: Calculate heat released by water when it cools down to the final temperature
Heat released by water = mass of water x specific heat of water x change in temperature
Heat released by water = 10g x 4.18 J/g°C x (100°C - final temperature)
Step 6: Equate the total heat absorbed and heat released to find the final temperature
Total heat absorbed = Heat absorbed by ice to reach its melting point + Heat absorbed by ice to melt + Heat absorbed by water to reach 100 degree Celsius + Heat absorbed by steam to condense
Total heat absorbed = 10.45 J + 1670 J + 2090 J + 11300 J
Total heat absorbed = 15070 J
Total heat released = Heat released by water when it cools down to the final temperature
Total heat released = 10g x 4.18 J/g°C x (100°C - final temperature)
Total heat released = 4180 J x (100°C - final temperature)
Equating heat absorbed and heat released:
15070 J = 4180 J x (100°C - final temperature)
Final temperature = 35.94°C
Answer:
The final temperature of the mixture is 35.94°C