Final answer:
The total energy required to completely melt a 25g ice cube at -8.0°C is 8590 J, after warming it to 0°C and then melting it.
Step-by-step explanation:
To calculate the energy required to completely melt a 25g ice cube at -8.0°C, we need to consider two energy conversions: first, warming the ice up to 0°C, and second, the melting process itself. We'll use the provided heat capacity (c) for ice and the heat of fusion (Hf) to calculate this.
Warming the Ice to 0°C
Energy to warm the ice (Q1): Q1 = m * c * ΔT
Where: m = mass of the ice = 25g
c = specific heat capacity of ice = 1.20 J/g°C
ΔT = change in temperature = 0°C - (-8.0°C) = 8.0°C
Q1 = 25g * 1.20 J/g°C * 8.0°C = 240 J
Melting the Ice
Energy to melt the ice (Q2): Q2 = m * Hf
Where: m = mass of the ice = 25g
Hf = heat of fusion of ice = 334 J/g
Q2 = 25g * 334 J/g = 8350 J
The total energy required to completely melt the ice cube is the sum of Q1 and Q2, which equals 240 J + 8350 J = 8590 J.