2. a cup of water and a bathtub full of water are at the same temperature, but have very different thermal…

Brief Explanations:

Thermal energy depends on temperature, mass, and specific heat capacity. Here, both are water (same specific heat capacity) and at the same temperature. But the bathtub has a larger mass of water. Since thermal energy formula (Q = mc\Delta T) (where (m) is mass, (c) is specific - heat capacity, (\Delta T) is temperature change, and here (\Delta T) is related to the internal state at a given temperature), with (c) and (\Delta T) (in terms of the state - related to temperature) the same, a larger (m) (bathtub) gives more thermal energy.

Answer:

The bathtub full of water has more thermal energy. Because thermal energy (Q = mc\Delta T), for water (same (c)), same temperature (so same (\Delta T) in terms of the state - related to temperature), and the bathtub has a larger mass (m) of water.