Heat transfer rates increase with temperature differences. If the temperature difference between the contenta and the surroundings doubles, the heat movement doubles (for conduction), and so does the rate of temperature change if you’re not dealing with phase change.
For each case, you have to define a starting temp, an ending temp, and a surroundings temp. In both cases we could set the surroundings to 22 C. For the hot case, we could say it starts at 80 C and cools to 55 C. And for the cold case we could start at 1 C and go to 8 C.
In the hot case, we are starting with a 58 C difference and ending with a 33 C difference between contents and surroundings.
In the cold case we are starting with a 21C difference and ending with a 14 C difference.
They may also be assuming an iced beverage in the cold case, and phase change for melting takes a toj of energy.
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