Final answer:
The specific latent heat of fusion of ice is 334 J/g. The energy needed to melt the remainder of the ice is 5.01 × 10^5 J. The final temperature of the mixture after an additional energy of 2 × 10^5 J is transferred is approximately 11.24°C.
Step-by-step explanation:
To determine the specific latent heat of fusion of ice, we can use the formula Q = mLf, where Q is the energy transferred to the ice, m is the mass of the ice block, and Lf is the specific latent heat of fusion. Given that half of the block melts, the mass of the melted ice is 1.5 kg (half of 3.00 kg). From the given information, we know that 5.01 × 10^5 J of energy is transferred to the ice block. Therefore, we can find the specific latent heat of fusion using the formula Lf = Q / (m * 1000). Substituting the values, we get Lf = (5.01 × 10^5 J) / (1.5 kg * 1000) = 334 J/g.
The energy needed to melt the remainder of the ice can be found using the formula Q = mLf, where Q is the energy needed, m is the mass of the remaining ice, and Lf is the specific latent heat of fusion. Since half of the ice already melted, the remaining mass of the ice is also 1.5 kg. Substituting the values, we get Q = (1.5 kg) * (334 J/g) * (1000 g/kg) = 5.01 × 10^5 J.
When an additional energy of 2 × 10^5 J is transferred to the mixture of ice and water, the temperature of the mixture will increase. To find the final temperature, we can use the formula Q = mcΔT, where Q is the energy transferred, m is the mass of the mixture, c is the specific heat capacity of water, and ΔT is the change in temperature. Since we are dealing with a mixture of ice and water, we need to consider the specific heat capacity of water during this process. The formula can be rearranged to find ΔT = Q / (m * c). Substituting the values, we get ΔT = (2 × 10^5 J) / ((3.00 kg + 1.5 kg) * (4.18 J/g°C) * (1000 g/kg)) ≈ 11.24°C. Therefore, the final temperature of the mixture will be 0°C + 11.24°C = 11.24°C.