Calculate the total heat required to melt 10 g of ice at 0°C and then raise its temperature to 10°C.

The formula for heat absorbed during a phase change (melting) is $Q_1 = mL_f$.
Given:

• Mass ($m$) = $10 \text{ g}$
• Latent heat of fusion ($L_f$) = $336 \text{ J/g}$

$$Q_1 = (10 \text{ g}) \times (336 \text{ J/g})$$ $$Q_1 = 3360 \text{ J}$$

The formula for heat absorbed during a temperature change is $Q_2 = mc_w\Delta T$.
Given:

• Mass ($m$) = $10 \text{ g}$
• Specific heat capacity of water ($c_w$) = $4.2 \text{ J/g K}$ (or $\text{J/g }^\circ\text{C}$)
• Change in temperature ($\Delta T$) = $10^\circ\text{C} - 0^\circ\text{C} = 10^\circ\text{C}$

$$Q_2 = (10 \text{ g}) \times (4.2 \text{ J/g }^\circ\text{C}) \times (10 ^\circ\text{C})$$ $$Q_2 = 420 \text{ J}$$

The total heat ($Q_{total}$) is the sum of the heat required for melting and the heat required for temperature increase.

$$Q_{total} = Q_1 + Q_2$$ $$Q_{total} = 3360 \text{ J} + 420 \text{ J}$$ $$Q_{total} = 3780 \text{ J}$$

The correct option is C.

$$\boxed{\text{C. } 3780 \text{ J}}$$