During the heat conduction lab experiment students were asked, among other things, to measure the

themal conductivity of two sample metal rods. Electrical heat was supplied at one end of the rod

and heat is extracted from the other end using a running cold water. The axial temperature along the

rod including the sample was measured using thernocouple probes mounted in the rod material.

Power was supplied to the electrical heater using a variable $AC$ transformer and students have

access to the maximum power supply as well as the power percentage when the steady state is

reached.

Typical data obtained by a group of students of your class are provided below

$I_{\text{m}\text{a}\text{x}}=210mA$

$U_{\text{a}\text{x}\text{x}}=230V$

Sample and Rod Diameter $D=25mm$

Temperatures are in $C$

$\%P$ : Power supply percentage

The bold temperatures are the temperatures located on the sample material

Questions

Why it is important the take the reading of the Power supply before the steady state can be

reached?

Give a physical explanation why the temperature is dropping sharply at the edge of the sample

$($ from T$3$ to T$4)$ and from $($T$6$ to T$7)$

Evaluate the conductivity of the sample for the three temperature experiments

From your own experience give an order of magnitude of the inaccuracy on the Power supply

Percentage and find out how it affects the accuracy of the thermal conductivity.

Assuming a linear variation of the conductivity with the temperature

$(T)=(T_0)(1+(T-T_0))$

find the experimental value of $.$