To understand the relationship between thermal energy, mass, and temperature, we need to consider the formula for thermal energy (often referred to as internal energy for solids). The thermal energy (U) of an object can be expressed as:
\[ U = mcT \]
Where:
- \( U \) is the thermal energy,
- \( m \) is the mass,
- \( c \) is the specific heat capacity, and
- \( T \) is the temperature.
Given that the large steel ball and the small steel ball have equal thermal energies, we can set up an expression based on their respective masses and temperatures:
For the large steel ball: \[ U_{\text{large}} = m_{\text{large}} c T_{\text{large}} \]
For the small steel ball: \[ U_{\text{small}} = m_{\text{small}} c T_{\text{small}} \]
Since both have equal thermal energies: \[ m_{\text{large}} c T_{\text{large}} = m_{\text{small}} c T_{\text{small}} \]
Assuming the specific heat capacity of steel is constant for both balls, we can simplify this to: \[ m_{\text{large}} T_{\text{large}} = m_{\text{small}} T_{\text{small}} \]
Now, since the large ball has a greater mass than the small ball (\( m_{\text{large}} > m_{\text{small}} \)), it follows that \( T_{\text{large}} \) must be less than \( T_{\text{small}} \) to maintain the equality.
Thus, the most likely true statement is:
The smaller ball has a higher temperature.