Final answer:
A bathtub full of water cools more slowly than a cup of water because it contains more heat, due to its larger mass and consequently higher heat capacity.
Step-by-step explanation:
A bathtub full of water cools more slowly than a cup full of water at the same temperature because the bathtub of water contains more heat than the cup of water. This phenomenon is related to the concept of heat capacity, which depends on both the mass of the object and its chemical composition. Since both the cup and bathtub contain water, they have the same specific heat capacity, but the bathtub, having a larger mass of water, has a higher total heat capacity.
The specific heat is the amount of energy required to raise the temperature of 1 gram of a substance by 1°C. Water has a high specific heat, which means it requires a lot of energy to change its temperature. Therefore, the greater volume of water in the bathtub can store more heat energy, and thus, it cools down more slowly than a cup of water.