Question: Consider a thermopile infrared detector having an active surface area A and initially at the ambient temperature T∞ (Fig.). The active sensing element (or, active junction, equivalently) of the detector consists of two very thin layers (δ2 + δ2 - 10-5 cm) of bismuth and tellurium formed by vacuum deposition onto a film of Mylar. The upper surface is suddenly subjected to a heat flux of q" [W/m2]. The heat transferred from the detector to a sink at a temperature Tsink via a connection may be approximated as = 0 (T - Tsink) [W] where 0 is a known quantity and T is the temperature of the detector active junction.
For a lumped detector active junction (bismuth and tellurium layers of thickness δ1 and δ2, respectively, and surface area A), neglecting the conductive loss to the Mylar as well as the convective and radiative losses to the ambient, determine
(a) the steady temperature,
(b) the unsteady temperature, and
(c) the time constant of the thermopile.