Given:
Initial temperature of ice,
![T_i=-25^(\circ)C](https://img.qammunity.org/2023/formulas/physics/college/w1i0xectmyxuczq04x75vot54io1413x7i.png)
Mass of ice,
![\begin{gathered} m=15\text{ g} \\ =0.015\text{ kg} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/5v3up43ubj9jy6jr483ehi8s5nh2dsawc1.png)
Final temperature,
![T_F=55^(\circ)C](https://img.qammunity.org/2023/formulas/physics/college/8o0nzsaewssbn4fpulhk2tr81ou91mzqbq.png)
The heat absorbed to bring the temperature of ice to 0°C is given as,
![Q_1=mC_i(0^(\circ)C-T_i)^{}](https://img.qammunity.org/2023/formulas/physics/college/pjccq8574j6lb1c68m09jpf0q5d44e6hmx.png)
Here, C_i is the specific heat of ice.
Substituting all known values,
![\begin{gathered} Q_1=0.015*2093*(0^(\circ)C-(-25^(\circ)C)) \\ =784.875\text{ J} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/wo6n8c59ux41mru896y11anwlrssjaf57d.png)
The heat absorbed to melt ice is given as,
![Q_2=mL](https://img.qammunity.org/2023/formulas/physics/college/hau8cfut5wpthxz84vfkkp436588al0lgk.png)
Here, L is latent heat of fusion of ice.
Substituting all known values,
![\begin{gathered} Q_2=0.015*33600 \\ =504\text{ J} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/7zoreytbjjzkakkys9q9hhiwt20y228uw6.png)
The heat absorbed by water to raise its temperature to 55°C is given as,
![Q_3=mC_w(T_F-0^(\circ)C)](https://img.qammunity.org/2023/formulas/physics/college/9mz4r91w33lvosqlswlj443e9w3tid1enw.png)
Here, C_w is the specific heat of water.
Substituting all known values,
![\begin{gathered} Q_3=0.015*4200*(55^(\circ)C-0^(\circ)C) \\ =3465\text{ J} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/9yj33n0g3d7ta0nrfpc3inwbmpq02qo05b.png)
Therefore, the heat absorbed the ice to raise the temperature for -25° C to 55°C is ,
![Q=Q_1+Q_2+Q_3](https://img.qammunity.org/2023/formulas/physics/college/sng9xykphdy5jf9hrjqyr9musk1fiwnxc4.png)
Substituting all known values,
![\begin{gathered} Q=784.875+504+3465 \\ =4753.875\text{ J} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/zz0vn5knpb4afftn869us176a1op4n11fv.png)
Therefore, the the heat absorbed the ice to raise the temperature for -25° C to 55°C is 4753.875 J.
Phase change diagram: