What energy is required to melt a block of ice at #0# #""^@C#, and raise the temperature of the water to #10# #""^@C#?

We could certainly do our own research on these, but since you seem uninterested, why should we?

To calculate the total energy required, we need to consider two steps:

1. The energy required to melt the ice at 0°C.
2. The energy required to raise the temperature of the resulting water from 0°C to 10°C.

For step 1, we use the heat of fusion (ΔHfus) of ice, which is 334 J/g. Since we have a block of ice, we need to multiply this by the mass of the ice.

For step 2, we use the specific heat capacity (c) of water, which is 4.18 J/g°C, and the temperature change (ΔT), which is from 0°C to 10°C. Again, we multiply this by the mass of the water.

Finally, we add the energies from both steps to get the total energy required.

Let's assume the mass of the ice block is 100 g:

1. Energy to melt the ice: (Q_1 = m \times \Delta H_{\text{fus}} = 100 , \text{g} \times 334 , \text{J/g} = 33400 , \text{J}).
2. Energy to raise the temperature of water: (Q_2 = m \times c \times \Delta T = 100 , \text{g} \times 4.18 , \text{J/g°C} \times 10°C = 4180 , \text{J}).

Total energy required = (Q_1 + Q_2 = 33400 , \text{J} + 4180 , \text{J} = 37580 , \text{J}).