The final temperature of the mixture of steam and ice can be calculated using the principle of conservation of energy. The heat lost by the steam will be equal to the heat gained by the ice, resulting in thermal equilibrium.
To solve for the final temperature, we will use the equation:
Qlost = Qgained
Where Qlost is the heat lost by the steam and Qgained is the heat gained by the ice.
The heat lost by the steam can be calculated using the equation:
Qlost = m x c x ΔT
Where m is the mass of the steam, c is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature.
Substituting the given values, we get:
Qlost = 10.0g x 4.18 J/g°C x (100°C - Tf)
Where Tf is the final temperature of the mixture.
The heat gained by the ice can be calculated using the equation:
Qgained = m x c x ΔT
Where m is the mass of the ice, c is the specific heat capacity of ice (2.09 J/g°C), and ΔT is the change in temperature.
Substituting the given values, we get:
Qgained = 50g x 2.09 J/g°C x (Tf - 0°C)
Where Tf is the final temperature of the mixture.
Now, equating Qlost and Qgained, we get:
10.0g x 4.18 J/g°C x (100°C - Tf) = 50g x 2.09 J/g°C x (Tf - 0°C)
Solving for Tf, we get:
Tf = 33.33°C
Therefore, the final temperature of the mixture of steam and ice is 33.33°C.
It is important to note that this calculation assumes that there is no heat loss to the surroundings and that the steam condenses completely into liquid water. In reality, some heat may be lost to the surroundings and not all of the steam may condense, resulting in a slightly lower final temperature.
