Thermal Conductivity of a Metal Rod

  • Thread starter Koshi
  • Start date
  • #1
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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?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Delphi51
Homework Helper
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That all sounds good but the devil is in the details. What answer did you get?
 
  • #3
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I got the answer 0.0022796947 w/(m*K)
 
  • #4
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is there anyone else who can help me find out where I went wrong?
 
  • #5
Astronuc
Staff Emeritus
Science Advisor
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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
 

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