How much heat is needed to turn $0.2\ \text{kg}$ of ice at $0\ ^\circ\text{C}$ into water at $30\ ^\circ\text{C}$? The latent heat of fusion of ice is $3.34 \times 10^{5}\ \text{J/kg}$, and $4180\ \text{J}$ warms $1\ \text{kg}$ of water by $1\ ^\circ\text{C}$.