Calculating Heat Conduction Time for a Wooden Cylinder on a Hot Plate

AI Thread Summary
To calculate the heat conduction time for a wooden cylinder on a hot plate, one must consider the thermal properties of wood, including its specific heat capacity and thermal conductivity. The heat transfer occurs primarily at the contact point with the hot plate, leading to a temperature gradient along the cylinder. The total heat required can be determined by integrating the heat needed for each segment of the cylinder as it reaches 523K. If the material were different, the thermal properties would change, affecting the heat conduction time. Understanding these principles allows for a more accurate estimation of the heating duration.
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If a wooden cylinder at 298K with perfectly insulated sides (other than the one in contact with the hot plate) where placed with one end on a hot plate until any point on the cylinder reached a temperature of 523K and the power of the hot plate is known and it all goes into the wood. How long would it take?

I created this question for an essay which is intended to go beyond the syllabus so my textbook does not cover this topic. I know that the temperature will first be reached at the part of the cylinder which is in contact with the hot plate, however I don't know the total amount of heat required because each part of the cylinder will reach a different temperature.
 
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