In certain thermocouple, the thermos emf is given by E = λθ + $\frac{1}{2} $ βθ2, where θ is the temperature of hot junction, λ = 10µV(0C)-1 and β = -0.05µV(0C)-2. If the cold junction temperature is 00C. Find the neutral temperature.

Solution:
At Neutral temperature, Thermo-EMF us maximum.
$\frac{dE}{dθ}$ = 0
Or, λ + $\frac{1}{2}$ β.2θ = 0
Or, λ + β.θ=0
Or, θ = $\frac{- λ}{β}$
Or, θ =$\frac{-10}{-0.05}$
∴ θ = 200⁰C