Thermal Properties/Heat Current

[verd]

Hi, I have a problem here that I've done, and am not sure if I have it correct. Here's the question:


A mixture of water and ice is in thermal equilibrium at temperature TW in a thermally insulated container at atmospheric pressure. A rod of aluminum (thermal conductivity k) has one end immersed in the mixture and the other one in contact with a system that is kept at constant temperature TH>TW (see figure). The rod has radius R for a length x from the system and then its radius is reduced to R/2. The total distance from the system to the top of the water-ice mixture is h. Note: the section of the rod that is immersed in the mixture is at the same temperature of the mixture and does not contribute to the thermal conductivity.

a) What is the temperature of the mixture TW in degree Celsius?
b) Calculate the temperature T of the rod at point A, where the radius changes.
c) Calculate the total heat current H through the rod.
d) Calculate the amount of ice that melts per second due to the heat transmitted through the rod.


Here is what I've done:
http://www.synthdriven.com/images/deletable/hwk3.jpg


Does this seem to be correct?? I'm a little shaky with these concepts and don't feel confident in these answers...


Thanks

 

[Nate810]

!Yes, your answers seem correct. However, you need to show the calculations that you used to arrive at the answers. That way, someone can check your work and make sure that your answers are correct.

 

[quicknote]

,

I would like to point out that your approach to the problem seems to be correct. However, there are a few things that you may want to consider. Firstly, when calculating the temperature of the rod at point A, it is important to take into account the change in radius as it will affect the thermal conductivity. Additionally, it would be helpful to include units in your calculations to ensure accuracy.

Regarding the total heat current, it is important to note that the heat current is not constant throughout the entire length of the rod. It will decrease as the radius decreases, so you may want to consider incorporating this in your calculation.

Lastly, when calculating the amount of ice that melts per second, it would be helpful to include the latent heat of fusion for water as it is a crucial factor in determining the amount of heat needed to melt ice.

Overall, your approach seems to be on the right track, but I would suggest double checking your calculations and considering these additional factors for a more accurate solution. Good luck!