Which statement best describes the relationship between thermal energy and temperature difference ($\mathrm{\Delta T}$)?

• A. Thermal energy transfer between two objects increases as the temperature difference ($\mathrm{\Delta T}$) between them increases.
• B. Thermal energy and temperature difference ($\mathrm{\Delta T}$) are always equal in magnitude ($\left|Q\right|=\left|\mathrm{\Delta T}\right|$).
• C. Thermal energy transfer is independent of temperature difference ($\mathrm{\Delta T}$).
• D. Thermal energy only exists when there is no temperature difference ($\mathrm{\Delta T}=0$).

Answer: (A)

Verified step by step guidance

1. Understand that thermal energy transfer (often denoted as Q) occurs due to a temperature difference (\Delta T) between two objects or systems.
2. Recall the concept of heat transfer: heat flows from the object at higher temperature to the one at lower temperature, and the rate of this transfer depends on the magnitude of the temperature difference.
3. Recognize that the greater the temperature difference (\Delta T), the greater the driving force for thermal energy transfer, meaning more heat will flow between the objects.
4. Note that thermal energy and temperature difference are not equal in magnitude; thermal energy depends on other factors such as the material properties and the amount of substance, not just \Delta T.
5. Conclude that the correct relationship is that thermal energy transfer increases as the temperature difference increases, which aligns with the physical principle of heat flow.