Question

identifying the relationship between mass and thermal energy transfer
which graph best demonstrates the general relationship between mass and temperature, similar to the trend of thermal energy absorbed by your sand and water samples?

Explanation:

Step1: Analyze the relationship between mass and thermal energy

According to the formula \(Q = mc\Delta T\) (where \(Q\) is thermal energy, \(m\) is mass, \(c\) is specific heat capacity, and \(\Delta T\) is temperature change). When thermal energy \(Q\) and specific heat capacity \(c\) are constant (assuming the same amount of heat is absorbed and same type of substance for simplicity in comparing the trend), \(\Delta T=\frac{Q}{mc}\), so \(\Delta T\) (temperature change) is inversely proportional to mass \(m\). As mass increases, the temperature change (assuming initial temperature is the same, so final temperature - initial temperature is related) will decrease.

Step2: Analyze each graph

• For the first graph: As mass increases, temperature decreases, which is in line with the inverse - proportional trend (when \(Q\) and \(c\) are constant).
• For the second graph: Temperature is constant as mass changes. This does not match the \(Q = mc\Delta T\) relationship (where \(\Delta T\) should change with \(m\) when \(Q\) and \(c\) are non - zero and constant).
• For the third graph: As mass increases, temperature increases. This is the opposite of the trend predicted by \(Q = mc\Delta T\) (when \(Q\) and \(c\) are constant)

Answer:

The first graph (the one where temperature decreases as mass increases) best demonstrates the relationship.