When a solid is heated, its volume generally increases due to thermal expansion. Let's go through the process step-by-step to understand what happens to the volume:
1. Initial State at 0°C:
- Let's denote the initial volume of the solid at [tex]$0^\circ C$[/tex] as \( v_1 \).
2. Heating the Solid to 100°C:
- When the solid is heated from [tex]$0^\circ C$[/tex] to [tex]$100^\circ C$[/tex], thermal expansion occurs.
- Due to this expansion, the volume of the solid increases from \( v_1 \) to a new volume, which we can denote as \( V_2 \).
3. Cooling the Solid Back to 0°C:
- Upon cooling the solid back down to [tex]$0^\circ C$[/tex], the molecules will return to their original positions if the material hasn't undergone any phase change or irreversible deformation.
- This means that the volume should revert to its initial state.
4. Final State at 0°C:
- After cooling back to [tex]$0^\circ C$[/tex], the volume of the solid will return to its initial volume \( v_1 \).
Therefore, the volume of the solid at [tex]$0^\circ C$[/tex] after heating to [tex]$100^\circ C$[/tex] and then cooling back to [tex]$0^\circ C$[/tex] will be \( v_1 \), not \( V_2 \). In simpler terms, heating and then cooling the solid will restore it to its original volume \( v_1 \) at [tex]$0^\circ C$[/tex].
Thus, the volume at [tex]$0^\circ C$[/tex] after this process will be [tex]\( v_1 \)[/tex].
