In a comparison of two pans of water, where pan A has 1 kg of water at 300 Kelvin and pan B has 2 kg of water at the same temperature, which pan has faster moving water molecules on average?

The correct choice indicates that the molecules in both pans are moving at the same average speed, and this is due to the temperature of the water in both pans. Temperature is a measure of the average kinetic energy of the water molecules. Since both pan A and pan B are at the same temperature of 300 Kelvin, the average kinetic energy—and thus the average speed—of the water molecules in both pans will be identical.

However, when it comes to thermal energy, pan B does have more of it because it contains a greater mass of water (2 kg compared to 1 kg in pan A). Thermal energy is related not just to the speed of the molecules (which is the same for both pans) but also depends on the mass of the substance.

So while the molecules are moving at the same speed in both pans due to their identical temperatures, the total thermal energy in pan B is greater because it has more mass. This reasoning supports the assertion that while the average speeds are the same, pan B indeed has more thermal energy due to its larger mass.