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

[PPMC]

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.

 

[bad_hair_day]

What would you do if it wasn't wood?

 

[Moetasim]

I would approach this problem by first understanding the fundamental principles of heat conduction. Heat conduction is the transfer of thermal energy between two objects or within an object due to a temperature difference. In this case, the hot plate is the source of heat and the wooden cylinder is the object that is being heated.

To calculate the heat conduction time for the wooden cylinder, we need to consider the material properties of wood, such as its thermal conductivity and specific heat capacity. These properties will determine how quickly the heat from the hot plate will be conducted through the cylinder.

We also need to take into account the dimensions of the wooden cylinder, such as its length and diameter, as these will affect the rate of heat conduction. Additionally, the temperature difference between the hot plate and the wooden cylinder will also play a role in determining the heat conduction time.

Once we have all of these factors, we can use the equation for heat conduction:

Q = kAΔT/t

Where Q is the amount of heat transferred, k is the thermal conductivity of wood, A is the cross-sectional area of the cylinder, ΔT is the temperature difference between the hot plate and the wooden cylinder, and t is the time for heat conduction.

Using this equation, we can calculate the time it would take for the wooden cylinder to reach a temperature of 523K. However, as you mentioned, different parts of the cylinder will reach different temperatures, so it is not a straightforward calculation. We would need to consider the temperature gradient within the cylinder and the rate at which heat is being conducted through each section.

In summary, calculating the heat conduction time for a wooden cylinder on a hot plate requires a thorough understanding of heat conduction principles and the material properties of wood. It is a complex problem that would require further experimentation and data collection to accurately determine the time it would take for the cylinder to reach a specific temperature.