ANSWERS: 2
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That's a tough one. On the one hand, the 80-degree room will warm the cold water faster because in addition to radiation and conduction, convection is also operating to transfer heat. On the other hand, radiative heat transfer depends on the difference of the *fourth power* of temperature, so those extra 10 degrees in the 90-degree room might transfer heat significantly more quickly. There are factors we don't know, such as the rate of air flow, the size and shape of the glass, etc, etc. So my final answer: It depends. In any case, one glass will reach its final temperature first, leaving the other to continue warming to its final temp. It might not be the same glass that *initially* warmed faster.
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I agree with xprofessor. Though my initial gut instinct was to say the glass in the 80 degree room. Purely because the heat remains moving arund the glass. However the rate of that movement will influence that effect.
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