Calculation of Final Temperature:
To calculate the final temperature of the mixture, we need to use the principle of heat transfer, which states that heat lost by one substance is equal to the heat gained by the other substance.

Heat lost by steam:
The steam at 100°C will lose heat as it cools down to the final temperature. The amount of heat lost can be calculated using the formula:

Q = m × c × ΔT

where Q is the heat lost, m is the mass of the steam, c is the specific heat capacity of water, and ΔT is the change in temperature.

Here, m = 10 g (mass of steam), c = 4.18 J/g°C (specific heat capacity of water), and ΔT = 100°C - final temperature.

So, the heat lost by the steam is:

Q1 = 10 × 4.18 × (100 - final temperature) Joules

Heat gained by ice:
The ice at 0°C will gain heat as it melts and then heats up to the final temperature. The amount of heat gained can be calculated using the formula:

Q = m × Lf + m × c × ΔT

where Q is the heat gained, m is the mass of the ice, Lf is the latent heat of fusion of water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Here, m = 50 g (mass of ice), Lf = 334 J/g (latent heat of fusion of water), c = 4.18 J/g°C (specific heat capacity of water), and ΔT = final temperature.

So, the heat gained by the ice is:

Q2 = 50 × 334 + 50 × 4.18 × final temperature Joules

Equating the heat lost and gained:
According to the principle of heat transfer, the heat lost by the steam must be equal to the heat gained by the ice. So, we can equate Q1 and Q2 to get:

10 × 4.18 × (100 - final temperature) = 50 × 334 + 50 × 4.18 × final temperature

Solving for final temperature, we get:

final temperature = 28.4°C

Explanation:
When the steam at 100°C is mixed with ice at 0°C, heat is transferred from the steam to the ice, causing the steam to cool down and the ice to melt and then heat up. This continues until the two substances reach a common final temperature. Using the principle of heat transfer and the formulas for calculating heat lost and gained, we can determine this final temperature to be 28.4°C.