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In both instances, they are approaching equilibrium with their surrounding temperature. It would require no input of energy for a cup of hot coffee to cool down (when it is hotter than its outside environment) or an ice cube to heat up (when it is cooler than its outside environment). Thus, both are spontaneous.
a cup of coffee is an open system in that the external temperature of the surroundings can affect the internal temperature of a system. A hot cup of coffee that exists in an area where the surrounding temperature is colder will allow for the heat transfer from the system to the surroundings.
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