The Thermoelectric Cave Explorer · AI Generator #GEN-35671AA6
Physics · thermodynamics
Problem
A geologist exploring a deep cave uses a thermoelectric generator to power her LED headlamp. The generator consists of two identical metal plates, each with area A=0.12m2 and thickness d=2.0mm, connected by thermoelectric elements. One plate is placed against the cave wall at temperature Tc=8°C, while the other is warmed by a small catalytic heater to temperature Th=45°C. The thermoelectric generator operates as a heat engine with efficiency η=0.08 times the Carnot efficiency. The thermal conductivity of each metal plate is k=180W/(m⋅K). In steady state, the electrical power output exactly equals the power dissipated by the LED headlamp. What is the electrical power generated by this thermoelectric device?