Question

which choice has the least thermal energy? a swimming pool full of cool water b bathtub full of warm water c all the water in earth’s oceans d cup of hot cocoa

Explanation:

Thermal energy depends on both temperature and mass (amount of substance). The formula related to thermal energy (for a substance) is \( Q = mc\Delta T \) (where \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is temperature change, but for comparing thermal energy, we consider mass and temperature).

Step1: Analyze each option's mass and temperature

• Option a: Swimming pool has a large mass (volume of water) but cool temperature.
• Option b: Bathtub has less mass than a pool but warm temperature.
• Option c: Earth's oceans have an extremely large mass (way more than pool, tub, or cup) with some temperature (generally above freezing, cool - warm range).
• Option d: Cup of hot cocoa has a very small mass (compared to pool, tub, oceans) and hot temperature.

Step2: Compare thermal energy

Thermal energy is the total kinetic energy of particles, so more mass (even at lower temp) can have more thermal energy than less mass at higher temp. Let's rank the masses: Oceans > Pool > Bathtub > Cup. The cup has the smallest mass, and even though it's hot, the small mass makes its total thermal energy the least. The pool (cool) has more mass than tub (warm) and cup (hot), so pool's thermal energy is more than cup. Oceans have way more mass than all, so their thermal energy is the most. Bathtub (warm) has more mass than cup (hot), so bathtub's thermal energy is more than cup. So the cup of hot cocoa has the least thermal energy.

Answer:

d. cup of hot cocoa