# Thermal Properties/Heat Current

1. Feb 7, 2006

### 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:

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

Thanks