Which of the following objects has more thermal energy?

• A. A cup of water at 90°C
• B. A pot of water at 50°C
• C. A bathtub of water at 40°C
• D. An ice cube at 0°C

Answer: (C)

Verified step by step guidance

1. Understand that thermal energy depends on both the temperature and the amount (mass) of the substance. Thermal energy is the total internal energy due to the motion of particles in a substance.
2. Recall the formula for thermal energy: \(Q = m \times c \times \Delta T\), where \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the temperature difference relative to a reference point (often taken as 0°C).
3. Compare the masses of the objects: a cup of water, a pot of water, and a bathtub of water have increasing amounts of water, so their masses increase in that order. The ice cube has a small mass.
4. Note the temperatures: 90°C (cup), 50°C (pot), 40°C (bathtub), and 0°C (ice cube). Although the bathtub has the lowest temperature among the liquid water options, its much larger mass can result in greater total thermal energy.
5. Conclude that the bathtub of water at 40°C has more thermal energy because the large mass compensates for the lower temperature, resulting in a higher total thermal energy compared to smaller amounts of hotter water or ice.