Question

two bottles of laundry detergent have the same mass and temperature. they are combined into one larger jug. the larger jug starts at the same temperature as the laundry detergent. the larger jug of laundry detergent has the same temperature as the original bottles of laundry detergent. the amount of thermal energy in the larger jug of laundry detergent is about ______ the amount of thermal energy in each of the smaller bottles of laundry detergent. options: the same as, twice, one - half

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

Original bottles: same mass (\( m \)), temp (\( T \)), so \( \Delta T = 0 \) (no temp change). Combined jug: mass \( 2m \), same \( c \), same \( \Delta T = 0 \).

Step3: Compare thermal energy

For each small bottle: \( Q_{\text{small}} = mc\Delta T \). For jug: \( Q_{\text{jug}} = (2m)c\Delta T = 2(mc\Delta T) = 2Q_{\text{small}} \).

Answer:

twice