Question

three buckets of sand have the same mass and temperature. they are combined into one larger bucket. the larger bucket of sand has the same temperature as the original buckets of sand. the amount of thermal energy in the larger bucket of sand is about ______ the amount of thermal energy in each of the smaller buckets of sand. options: the same as, three times, one - third

Explanation:

Step1: Recall thermal energy formula

Thermal energy \( Q = mc\Delta T \), where \( m \) is mass, \( c \) is specific heat, \( \Delta T \) is temperature change.

Step2: Analyze given conditions

Each small bucket: mass \( m \), temp \( T \), so \( Q_{small}=mc(T - T_0) \) ( \( T_0 \) is reference temp). Combined: mass \( 3m \), temp \( T \), so \( Q_{large}=3mc(T - T_0) \).

Step3: Compare \( Q_{large} \) and \( Q_{small} \)

\( Q_{large}=3\times(mc(T - T_0)) = 3Q_{small} \).

Answer:

three times