Finding thermal conductivity of an insulated metal bar

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SUMMARY

The discussion focuses on calculating the thermal conductivity (K) of an insulated metal rod, where one end is maintained at 100°C and the other at 0°C. The rod's dimensions are 60.0 cm in length and 1.40 cm² in cross-sectional area. The heat conducted by the rod melts 7.15 g of ice in 15 minutes, leading to a calculated thermal conductivity of 114 W/m*K after correcting for unit conversion errors. The initial miscalculation of 1.14 W/m*K was resolved by properly accounting for the conversion factors.

PREREQUISITES
  • Understanding of thermal conductivity and its significance in heat transfer.
  • Familiarity with the heat conduction equation: (Heat/time) = k(A)(ΔT/L).
  • Knowledge of unit conversions, particularly between metric and SI units.
  • Basic principles of phase change, specifically the heat of fusion for water.
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  • Study the derivation and application of Fourier's law of heat conduction.
  • Learn about the impact of material properties on thermal conductivity.
  • Explore advanced heat transfer topics, including transient heat conduction.
  • Investigate methods for measuring thermal conductivity in various materials.
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Students in physics or engineering, particularly those studying heat transfer, as well as professionals involved in thermal analysis and material science.

reed2100
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Homework Statement



One end of an insulated metal rod is maintained at 100∘C and the other end is maintained at 0.00 ∘C by an ice–water mixture. The rod has a length of 60.0cm and a cross-sectional area of 1.40cm2 . The heat conducted by the rod melts a mass of 7.15g of ice in a time of 15.0min .
Find the thermal conductivity K of the metal.

Homework Equations



(Heat/time) = k(A)(ΔT/L)
H(fusion) for water = 334 KJ/kg*K = 334000 J/kg

The Attempt at a Solution



Converting to SI units -> L=.6 m, A= .014 m^2, m(ice) = .00715 kg, time= 900s

Q=heat/time, so heat = .00715 kg(334000 J/kg) = 2388 J, Q = 2388J/900s = 2.6533 J/s = 2.653W

So, 2.653 W = k(.014 m^2)(100°C/.6m)

2.653 W / ( .014 m^2 ) *.6m / 100 C ≈ 1.14 W/m*C OR 1.14W/m*K since K or C can be used interchangeably here.

So, my answer kept coming up as 1.14, yet the correct answer was 114 W/m*K.

I am confused as to why I'm getting the correct answer in a sense but with my order of magnitued off. It makes me wonder if I'm doing my math correctly or I made a careless mistake somewhere. Any and all help/advice will be greatly appreciatied.
 
Last edited:
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reed2100 said:
A= .014 m^2
Try that one again.
 
Oh, I completely forgot to divide by 100 twice. I'm getting the right answer now, thanks!
 

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