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 more mass. According to the formula \(Q = mc\Delta T\) (where \(Q\) is thermal energy, \(m\) is mass, \(c\) is specific - heat capacity, and \(\Delta T\) is the change in temperature from a reference point, here assume \(\Delta T\) is non - zero and same for both as they are at the same temperature above the reference). Since \(c\) and \(\Delta T\) are the same and \(m_{bathtub}>m_{cup}\), the bathtub has more thermal energy.

Answer:

The bathtub full of water has more thermal energy. Because thermal energy (\(Q = mc\Delta T\)) depends on mass (\(m\)), specific heat capacity (\(c\)), and temperature change (\(\Delta T\)). Both are water (\(c\) is the same) and at the same temperature (so \(\Delta T\) is the same relative to a reference). But the bathtub has a larger mass (\(m\)), so by the formula \(Q = mc\Delta T\), it has more thermal energy.