To calculate the change in internal energy as ice is changed to water at 0°C, we need to consider the specific heat capacity of ice and water and the latent heat of fusion.
The specific heat capacity (c) of ice is approximately 2.09 J/g°C, and the specific heat capacity of water is about 4.18 J/g°C. The latent heat of fusion (Lf) for water is 334 J/g.
First, let's calculate the change in internal energy as the ice is warmed from 0°C to its melting point:
ΔU_ice = mass × c_ice × ΔT_ice = 5.0 g × 2.09 J/g°C × (0°C - 0°C) = 0 J
Since there is no temperature change within the ice, the change in internal energy is zero.
Next, we calculate the heat needed to melt the ice:
Q_melt = mass × Lf = 5.0 g × 334 J/g = 1670 J
Therefore, the heat needed to melt the ice is 1670 Joules.
It's important to note that these calculations assume ideal conditions and neglect any losses due to the surrounding environment.