Steam at 100°C is added to ice at 0°C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 10. g and the mass of ice is 50. g. (b) What If? Repeat when the mass of steam is 1.g and the mass of ice is 50.g.
To answer these questions, we need to apply the principles of energy conservation and phase changes.
(a) Given:
Mass of steam (msteam) = 10 g
Mass of ice (mice) = 50 g
To find the amount of ice melted and the final temperature, we can follow these steps:
Step 1: Calculate the heat transferred from steam to ice (Q):
Q = msteam * Csteam * ΔT
Where:
Csteam is the specific heat capacity of steam, approximately 2.03 J/g°C.
ΔT is the change in temperature from the boiling point of water, which is 100°C, to the final temperature.
Step 2: Calculate the heat required to melt the ice (Qmelt):
Qmelt = mice * Lfusion
Where:
Lfusion is the heat of fusion for ice, approximately 334 J/g.
Step 3: Equate the heat transferred (Q) to the heat required for melting (Qmelt):
Q = Qmelt
Step 4: Solve for the final temperature (Tf):
Q = Qmelt
msteam * Csteam * ΔT = mice * Lfusion
(10 g) * (2.03 J/g°C) * (Tf - 100°C) = (50 g) * (334 J/g)
(Tf - 100°C) = (50 g * 334 J/g) / (10 g * 2.03 J/g°C)
(Tf - 100°C) = 1655.67°C
Tf = 1755.67°C
However, this result seems unrealistic, as water boils at 100°C and cannot reach such a high temperature. It is likely that some assumptions or data are incorrect.
(b) Given:
Mass of steam (msteam) = 1 g
Mass of ice (mice) = 50 g
We can follow the same steps as above to find the new final temperature:
Step 1: Calculate the heat transferred from steam to ice (Q):
Q = msteam * Csteam * ΔT
Step 2: Calculate the heat required to melt the ice (Qmelt):
Qmelt = mice * Lfusion
Step 3: Equate the heat transferred (Q) to the heat required for melting (Qmelt):
Q = Qmelt
Step 4: Solve for the final temperature (Tf):
Q = Qmelt
msteam * Csteam * ΔT = mice * Lfusion
(1 g) * (2.03 J/g°C) * (Tf - 100°C) = (50 g) * (334 J/g)
(Tf - 100°C) = (50 g * 334 J/g) / (1 g * 2.03 J/g°C)
(Tf - 100°C) = 8268.47°C
Tf = 8368.47°C
Again, this result is unrealistic, as water cannot reach such a high temperature. It is important to double-check the provided data or assumptions as they seem to be inaccurate.
Please note that water is expected to reach its boiling point of 100°C during this process, and any further heat will only result in phase change (evaporation) rather than a rise in temperature beyond the boiling point.