When transferring heat from a cold substance to a hotter substance, what must be supplied?

The concept of transferring heat from a cold substance to a hotter substance revolves around the principles of thermodynamics. In general, heat naturally flows from high-temperature areas to low-temperature areas. However, if you want to transfer heat from a cold substance to a hot one, you need to supply external work to overcome this natural flow.

This process is often utilized in refrigerators and heat pumps, where mechanical work is done to move heat against its natural gradient. For instance, in a refrigerator, a compressor does external work to transfer heat from the inside (cold) to the outside (hot). This means that without external work being supplied, the heat transfer would not occur in the desired direction.

The other choices involve concepts that do not apply to the situation. Internal energy refers to the total energy contained within a substance, but simply having this energy does not enable heat transfer against its natural direction. Higher temperature and lower temperature refer to the states of the substances involved but do not address the necessity of energy input to move heat from cold to hot. Therefore, the requirement of external work is fundamental to facilitate this unconventional heat transfer.