A little guidance with thermal conductivity please

[earlofwessex]

a little guidance with thermal conductivity please...

Homework Statement

there isn't really a problem statement, as its a lab write up I'm doing.
we had two blocks of the same metal, one at room temp and one at a fixed temp of almost 50 degrees.

a Rod of different metal was put between the metal blaocks and the temperature measured. I'm looking to calculate the thermal conductivity of the rod. but the problem is that I'm out by a factor of almost 1000.

Homework Equations

dE/dt = M C dTheta/dt.
(change in energy = Mass x SpecificHeatCapacity x Change in Temp)

Phi = Lambda A dTheta/dX
(heat energy (W) = thermal conductivity x Area x Temperature Gradient)

The Attempt at a Solution

ok, so we're given an electric heater which cuts off at about 41 degrees, (heating up the block without attatched rod et.c gives Specific heat capacity from W=IV=M C dtheta/dt)

I'm getting 630 j/kg/K, where as its probably alluminium at 900ish. that's fine, heat lost to surroundings and so on. (but would it be better to use the official value or the calculated value for the next bit?)

so examining the cold block now that the system is set up, we can get dE/dt.
this has to be energy flowing through the rod right? so
M C dtheta/dt=Lambda A dTheta/dx

M = mass of the cold block
C = SHC of the coldd block
dTheta/dt of the cold block
Lambda of the rod
A = cross sectional area of the rod.
dTheta/dx = temperature gradient of the rod.

except that... dTheta/dx changes with time (as the cold block heats up).

so the time derivative of both sides...
dW/dt = Lambda A (dTheta/dx)/dt

where dW/dt is the change in watts over time for the block of alluminium.

this equation is giving me a value for lambda of about 1 watt per metre per kelvin. but the rod is definitely metal, and looks like copper, so the result should be up to 380. what am i doing wrong? is it better to use the published value for Specific heat capacity of alluminium? that still wouldn't get me any closer...


thanks

 

[earlofwessex]

Bump...

I can post some figures if it would help?

this is a diagram of the setup roughly...

 

[nlightner]

for any help.

I can provide some guidance on thermal conductivity. Firstly, it is important to make sure that all the measurements and calculations are accurate. Any discrepancies could be due to errors in measurement or calculation. It is always better to use published values for specific heat capacity and thermal conductivity, as they are more accurate and reliable.

In addition, the temperature gradient (dTheta/dx) should be calculated at a specific point in time, rather than over a period of time. This will give a more accurate value for the thermal conductivity of the rod.

It is also important to consider the properties of the materials involved. Different metals have different thermal conductivities, so it is possible that the rod is made of a metal with a lower thermal conductivity than copper. This could explain the lower value obtained for thermal conductivity.

Lastly, it would be helpful to double check the setup and procedure of the experiment to ensure that all variables are controlled and measured accurately. If necessary, repeating the experiment with different materials or setups could also provide more accurate results.

In summary, to accurately calculate thermal conductivity, it is important to use published values, calculate the temperature gradient at a specific point in time, and consider the properties of the materials involved. It is also crucial to ensure accurate measurements and control of variables in the experiment.