2
Midterm 1
An engineer is shopping for a temperature sensor with a certain response time. One temperature probe is shaped
like a cylinder of some unknown diameter and a length of 10 cm. The probe is made of chromel, with properties listed
in the table below. The temperature probe is advertised as having a response time of $0.65$ s. The engineer plans to
use the probe in a system with $h = 565 \text{ W m}^{-2} \text{K}^{-1}$.
Determine the diameter of the probe. Is it reasonable to assume the probe will be at uniform temperature across its
cross-section?
Property
Value
Density, $\rho$
8500 kg m$^{-3}$
Specific heat, c
440 J kg$^{-1}$ K$^{-1}$
Thermal conductivity, k
19 W m$^{-1}$ K$^{-1}$