If you put melted ice cream back into the freezer, it will not be as big as before it melted. When ice cream melts, it undergoes a physical change from a solid to a liquid state. During this process, the ice crystals present in the ice cream break down and the air incorporated into the mixture is released, causing the ice cream to lose its original volume.
The freezing process works by lowering the temperature of the ice cream, turning the liquid back into a solid state. However, the re-frozen ice cream will not have the same structure and texture as the original. The ice crystals formed during the re-freezing process are larger and less uniform than the ones in the original ice cream, which results in a different texture and a less creamy mouthfeel.
Additionally, the freezing and thawing cycles can cause further degradation in the quality of the ice cream, leading to the formation of ice crystals and the separation of ingredients, which may negatively impact the taste and texture.
Therefore, while the re-frozen ice cream will be solid again, it will not regain its original volume or quality after melting and refreezing. It's generally best to consume melted ice cream promptly or discard it if it has been sitting out for too long to maintain its optimal taste and texture.