Thermal Conductivity of a Metal Rod

[Koshi]

Homework Statement

One end of an insulated metal rod is maintained at 100^\circ C and the other end is maintained at 0.00 ^\circ {\rm C} by an ice–water mixture. The rod has a length of 75.0 cm and a cross-sectional area of 1.40 cm^2. The heat conducted by the rod melts a mass of 7.85 g of ice in a time of 15.0 min. Find the thermal conductivity k of the metal.

Homework Equations

H=dQ/dt=kA(T₂-T₁)/L

The Attempt at a Solution

I tried to solve for k using the formula for heat transfer and since H was not given, I substituted it with dQ/dt. Then in stead of dQ I used the equation for heat transformation Q=mL where m=mass of ice melted and L=333kj/kg which is the heat of fusion for water, if I'm not mistaken. I put everything in SI units and solved but I got the wrong answer. Did I make a wrong assumption somewhere?

 

[Delphi51]

That all sounds good but the devil is in the details. What answer did you get?

 

[Koshi]

I got the answer 0.0022796947 w/(m*K)

 

[Koshi]

is there anyone else who can help me find out where I went wrong?

 

[Astronuc]

Please show one's work, particularly, the value obtained for heat flux. If one is off by 4-orders of magnitude, look at the value for cross-sectional area given in cm² and make sure it is properly converted to m².

I obtain a value on the order of the thermal conductivity of a metal. Thermal conductivity of Al is about 200 W/m-K, and that of Cu is about 385 W/m-K.

Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html#c1