A

The system consists of 1 kg of ice at 0ºC and 1 kg of water at 10ºC.
Step 1: When the ice and water are mixed, heat will flow from the warmer water to the colder ice until thermal equilibrium is reached.
Step 2: The heat lost by the water can be calculated using the formula:
$$ Q = mc\Delta T $$
where m is the mass, c is the specific heat capacity of water (4.18 kJ/kgºC), and \Delta T is the change in temperature.
Step 3: The heat gained by the ice must equal the heat lost by the water. The ice will absorb heat to melt and to raise the temperature of the resulting water to 0ºC.
Step 4: Calculate the heat lost by the water:
$$ Q_{lost} = m_{water} \cdot c_{water} \cdot (T_{initial} - T_{final}) \Rightarrow Q_{lost} = 1 \cdot 4.18 \cdot (10 - 0) = 41.8 kJ $$
Step 5: The heat gained by melting the ice at 0ºC can be calculated with:
$$ Q_{gained} = m_{ice} \cdot L_f \Rightarrow Q_{gained} = 1 \cdot 334 kJ = 334 kJ $$
The heat lost by the water equals the heat gained by the ice when thermal equilibrium is reached at 0ºC.
Step 6: Since the final temperature of the mixture is found to remain at 0ºC, the heat exchange calculations confirm that the ice melts, absorbing the right amount of heat from the warmer water without increasing the temperature beyond 0ºC.
Therefore, the melting of ice and the mixing of water at 0ºC establishes the equilibrium state.