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

[cyberdx16]

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...

 

[chaoseverlasting]

looks right.

 

[m2003]

I would first like to clarify that the problem statement mentions an "ideal gas," which means that the gas behaves according to the ideal gas law, PV = nRT. This is important to note because the thermal conductivity of a gas is different from that of a solid material, so the solution provided may not be accurate for an ideal gas.

Moving on to the solution provided, it appears to be correct in terms of using the correct formula and plugging in the given values. However, I would like to point out that the units used for the cross-sectional area of the rod are incorrect. It should be in square meters (m^2), not centimeters (cm^2). This may have been a simple mistake, but it is important to use the correct units in scientific calculations.

Additionally, for the second part of the problem, it is important to note that the thermal conductivity of a material can vary with temperature. Therefore, using the same thermal conductivity value may not give an accurate solution for a different temperature. It would be more accurate to use a thermal conductivity value that is specific to the temperature of the oven. This could be obtained from a thermal conductivity vs. temperature graph or from a table of thermal conductivity values for different temperatures.

Overall, the solution provided is a good attempt and the correct answer was obtained. However, it is important to pay attention to units and to consider the variation of thermal conductivity with temperature in order to obtain more accurate results.