Measuring Thermal Conductivity by Ångstrom’s Method

In this experiment, κ, the thermal conductivity of a rod of brass, was measured by periodically heating one end of the rod. Turning the heater attached to the rod on and off with a 10 mHz square wave signal, waves of heat were sent along the length of the rod, measured by two thermistors a distance ∆x apart. Taking these temperatures as a function of time, a Fourier transform was applied to a 15 period long segment of data, allowing us to use the amplitudes γn and phases φn of the first three harmonics to make three distinct measurements of the thermal conductivity of the brass rod. For the first three contributing harmonics in the Fourier transform, n = 1, n = 3, and n = 5, an average thermal conductivity value of κ̄ ± σκ = 103 ± 2 W/(m K) was found. This result gives a small error of 5% with regards to the accepted value of κ = 109 W/(m K).