The phenomenon you're observing, where an empty bottle becomes colder than a full one when both are placed in the freezer together, can be explained by the concept of thermal conductivity and specific heat capacity.
Thermal conductivity refers to the ability of a material to conduct heat. Different substances have different thermal conductivities, meaning they transfer heat at different rates. In this case, the bottle and its contents (whether empty or full) are likely made of different materials.
When you place the bottles in the freezer, heat from both the bottle and its contents needs to be transferred to the colder surroundings. Since the empty bottle has less mass compared to the full bottle, it generally has a lower specific heat capacity.
Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. Substances with lower specific heat capacities heat up or cool down more quickly than substances with higher specific heat capacities.
Given that the empty bottle has less mass and thus lower specific heat capacity, it can cool down more rapidly than the full bottle. The reduced amount of material in the empty bottle allows for quicker heat transfer, causing it to reach a lower temperature compared to the full bottle.
Additionally, the liquid inside the full bottle provides some insulation, as liquids generally have higher specific heat capacities than the bottle material. This insulation slows down the cooling process, preventing the liquid from reaching the same low temperature as the empty bottle.
In summary, the differences in thermal conductivity and specific heat capacity between the bottle material and its contents result in the empty bottle becoming colder than the full one when placed in the freezer together.