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A cup with 
boiling water will reach room temperature faster than a cup with ice. 
Here is the explanation:
  1. Greater Temperature Difference: The boiling water has a much larger temperature difference relative to room temperature than the cup with ice.
  2. Rate of Heat Transfer: Heat transfer is proportional to the temperature gradient. The larger the initial temperature difference, the faster the rate at which heat is lost from the hotter object to the surroundings.
  3. Phase Change Delay (Ice): The cup with ice must go through a phase change (melting) before the water temperature can begin to rise significantly toward room temperature. This melting process requires a substantial amount of energy (latent heat of fusion), which slows down the overall warming process compared to the rapid cooling of the boiling water. 
Nov 4, 2016 — Your second and third questions go hand in hand, because room temperature can affect insulation. The greater the temperature difference between two o...
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