Final answer:
The 20-gram water sample's temperature will increase less than the 10-gram sample when the same amount of thermal energy is added, because the larger mass requires more energy for the same temperature change.
Step-by-step explanation:
The temperature of a 20-gram sample of water would change less than a 10-gram sample if the same amount of thermal energy is added to both. This is due to the specific heat capacity of water, which is the amount of heat required to raise the temperature of a substance. Since the 20-gram sample has more mass, it requires more energy to increase its temperature by the same amount as the 10-gram sample. Therefore, under the same energy addition, the 10-gram sample's temperature will increase more than the 20-gram sample.