Question

1. a cup of water and a bathtub full of water are at the same temperature, but have very different thermal energies. which one has more thermal energy? explain why.

Explanation:

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.