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The figure below shows a 1000-milliliter dewar flask filled with water, with thermal probes at the top and the bottom. The temperature of the water is 26oC (around room temperature), as measured by both probes and seen on the large digital displays at the right in the photograph. An electric heater is positioned near the top of the water. When the heater is turned on, it begins to heat the water. As time goes by, measured in seconds by the digital timer at the left in the photograph, we can measure the temperature of the water at the top and the bottom of the dewar, displaying the temperature of the water at the top and the bottom of the dewar as a function of elapsed time. Click on the photograph below to see a video of the action (or lack thereof) for the first few seconds.

Perhaps it is appropriate to share a few numbers: the volume of the dewar is 1000 ml; the heater draws a little over 1 ampere at 110 VAC (60 Hz) so that it produces about 125 Watts of heating.

 q314

The question this week involves how the temperature of the water near the top and near the bottom of the dewar will change with time as the heater heats the water near the top of the dewar.

Part 1: After about thirty minutes (1800 seconds) the temperature of the water near the top of the dewar will be:

  • (a) less than 26oC.
  • (b) about 26oC.
  • (c) about 30oC.
  • (d) about 50oC.
  • (e) about 75oC.
  • (f) almost 100oC.

Part 2: After about thirty minutes (1800 seconds) the temperature of the water near the bottom of the dewar will be:

  • (a) less than 26oC.
  • (b) about 26oC.
  • (c) about 30oC.
  • (d) about 50oC.
  • (e) about 75oC.
  • (f) almost 100oC.

On or after February 13, click Read More for the answer.

Part 1: The answer is (f): almost 100o.

Part 2: The answer is (b): about 26o.

This can be seen in an mpeg video by clicking your mouse on the photograph below, which is a frame of the video after exactly 30 minutes (1800 seconds). (Note that the video is speeded up during most of the 1800 seconds duration; you don't actually have to watch for half an hour!)

q314a

This phenomenon arises due to (1) heat radiation from the top of the dewar, (2) the poor conductivity of water, and (3) the fact that hot water is less dense than cold water, so hot water naturally will "float" on cooler water. Sometimes when you swim in a lake or river you may notice that the top surface of the water is warm, but the water down below, where you can stick your feet, may feel much cooler.