How Do You Calculate Thermal Conductivity in a Heated Metal Rod?

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SUMMARY

The thermal conductivity of the metal rod connecting an oven to a cylinder filled with ideal gas was calculated to be 9 W/m·K. The setup involved a square rod with a side length of 1 cm and a length of 2.3 m, with the oven temperature at 750 K and the gas temperature at 450 K. The heat current conducted through the rod was measured at 27 W. The formula used for calculation was H = k*A*(T2-T1) / L, confirming the derived value of k as accurate for subsequent calculations.

PREREQUISITES
  • Understanding of thermal conductivity and its units (W/m·K)
  • Familiarity with heat transfer equations, specifically H = k*A*(T2-T1) / L
  • Basic knowledge of geometry for calculating cross-sectional area of a square rod
  • Concept of ideal gas behavior and temperature effects on heat transfer
NEXT STEPS
  • Research the impact of material properties on thermal conductivity
  • Explore advanced heat transfer concepts, such as convection and radiation
  • Learn about thermal conductivity measurement techniques for various materials
  • Investigate the effects of temperature gradients on heat transfer efficiency
USEFUL FOR

Students in physics or engineering disciplines, thermal engineers, and professionals involved in heat transfer applications will benefit from this discussion.

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Homework Statement



A cylinder with a piston is filled with ideal gas. The gas temperature is held at 450 K. The cylinder is heated by an oven through a square metal rod connected between the oven and the cylinder. The rod has sides d = 1 cm and length L = 2.3 m.

(a) If the oven is held at 750 K, and the heat current conducted through the metal rod is 27 W, find the thermal conductivity of the metal in the rod.

k = W/m K
9 NO

HELP: H = k*A*(T2-T1) / L

HELP: H is the heat current; k is thermal conductivity; T2 and T1 are temperatures at two ends; A and L are cross-sectional area and length of the rod.

Homework Equations



H = k*A*(T2-T1) / L

The Attempt at a Solution



27=k(.023m^2)(300k)/2.3m

k=9

I'm pretty sure I am right here... the following quesion asks,

For a larger cylinder at 450 K, a heat current of 57 W is needed. If we use the same metal rod to conduct heat, find the oven temperature in Kelvin that will maintain the necessary heat current.

and i used the k value 9 and gave me an answer 1083.3, which was the correct answer...
 
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looks right.
 

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