Answer:
The final temperature of the mixture is 24.2C. Since the final temperature is above the melting point of ice (0C), the ice will have melted and the final phase of the mixture will be liquid water.
Step-by-step explanation:
First, we can calculate the energy required to melt the ice into water:
Q1 = mL,
where Q1 is the energy required, m is the mass of the ice, and L is the latent heat of fusion of ice, which is 334 kJ/kg.
Q1 = 0.50 kg x 334 kJ/kg = 167 kJ
Next, we can calculate the energy required to heat the ice from -100C to 0C:
Q2 = mcΔT,
where Q2 is the energy required, m is the mass of the ice, c is the specific heat capacity of ice, which is 2.108 J/gC, and ΔT is the change in temperature.
Q2 = 0.50 kg x 2.108 J/gC x (0C - (-100C)) = 105,400 J = 105.4 kJ
Now, we can calculate the energy required to heat the water from 20C to the final temperature T:
Q3 = mcΔT,
where Q3 is the energy required, m is the mass of the water, c is the specific heat capacity of water, which is 4.184 J/gC, and ΔT is the change in temperature.
Q3 = 3.0 kg x 4.184 J/gC x (T - 20C)
Finally, we can set the total energy input to the system equal to the total energy required:
Q1 + Q2 + Q3 = 0
Substituting the values we calculated above and solving for T, we get:
167 kJ + 105.4 kJ + 3.0 kg x 4.184 J/gC x (T - 20C) = 0
T = 24.2C
Therefore, the final temperature of the mixture is 24.2C. Since the final temperature is above the melting point of ice (0C), the ice will have melted and the final phase of the mixture will be liquid water.