Final answer:
After adding 65.0 kilojoules of energy to 150g of ice at 0.0°C, all the ice will melt, and the remaining energy will raise the temperature of the water to approximately 23.98°C.
Step-by-step explanation:
To determine the final temperature of the water after adding 65.0 kilojoules of energy to 150g of ice at 0.0°C, we must consider the specific heat capacity of ice and water, as well as the latent heat of fusion for ice melting into water. The heat required to melt ice is 333.55 kJ/kg, and the specific heat capacity of water is 4.18 kJ/kg°C. Initially, the energy will go into melting the ice. If all the ice melts and there is still energy left, this will raise the temperature of the resulting water.
First, calculate the energy needed to melt the ice:
Energy required to melt 150g of ice = (150g / 1000g/kg) × 333.55 kJ/kg = 49.9825 kJ
Since 65.0 kJ is greater than 49.9825 kJ, all the ice will melt, and we have an excess energy of:
Excess energy = 65.0 kJ - 49.9825 kJ = 15.0175 kJ
Now, use the specific heat capacity to find how much the temperature of the water will increase:
ΔT (increase in temperature) = Excess energy / (Mass of water × Specific heat capacity of water)
ΔT = 15.0175 kJ / (0.150 kg × 4.18 kJ/kg°C) = 23.98°C (approximately)
Therefore, the final temperature of the water will be the sum of the initial temperature and the increase:
Final temperature = 0°C + 23.98°C
= 23.98°C