Can Heat Pumps Operate Without a Work Input?

Just because a cycle obeys the 1st Law does not guarantee that the cycle will occur.
QH
QC
QC
QH
WS
HP
Two cycles operate between the same two thermal reservoirs.  The cycle on the left represents the spontaneous transfer of heat from a hot reservoir to a cold reservoir.  The heat pump cycle on the right illustrates the fact that a heat pump requires a work input to make heat flow out of a cold reservoir and into a hot reservoir.  This does not happen spontaneously.
  • Heat flow from a hot reservoir to a cold reservoir requires only a medium for the heat to flow through.
  • This process obeys the 1st Law and occurs spontaneously.
A heat pump or refrigeration cycle transfers heat from a cold reservoir to a hot reservoir.
Is it possible for a heat pump or refrigerator to operate without any work input?

NO!

Although such a process obeys the 1st Law, heat does not spontaneously flow from a cold reservoir to a hot reservoir.

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Ch 6, Lesson C, Page 2 - Can Heat Pumps Operate Without a Work Input?