Final answer:
Thermal energy between Substance x and Substance w can be transferred through radiation without direct contact, which aligns with the presented information on heat transfer methods and thermal conductivity.
Step-by-step explanation:
Given the information about methods of heat transfer such as conduction, convection, and radiation, and the property of thermal conductivity, we can assess how thermal energy is exchanged between substances. Conduction requires direct physical contact between materials, and is typically prominent in materials that are good conductors of electricity, such as metals. Radiation involves the transfer of energy through electromagnetic waves and does not require materials to be in contact or mixed. For instance, the Sun heats the Earth through radiation. Therefore, among the given statements, the one that is best supported by the data is that Substance x will transfer thermal energy to Substance w through radiation if they are placed near each other, since this method of heat transfer does not necessitate the substances being in physical contact.