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Question

If water temperatures 80oC and 60oC is closed in two different vessels, which water gets cooled faster ?

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Solution

Of course, the vessel the containing the water at 600C will cool faster because it will need to lose less energy to cool down to a certain temperature.
The water of temperature 800C will first need to lose its energy and gain 600C following to which it will lose further until a certain temperature.
Hence, more time is needed to lose more energy and less time is needed to lose less energy. So 800C of water will need more time to cool down and water at 600C will need less time to cool down.

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