The temperature of inversion of a thermocouple is 620^oC and the neutral temperature is 300^oC. What is the temperature of cold junction

-20°C

Let e = α (θ – θ_C) + β (θ²– θ²_C )

where θ_C = temperature of cold junction

at inversion temperature e = 0

⇒ θ_i = – θ_C – α/β

at neutral temperature : \(\frac{de}{dθ} = 0 \)

⇒ θ_n = – α/2β

θ_i = – α/β– θ_C

⇒ θ_i = 2θn – θc 

⇒ \(\theta_n = \frac{\theta_i + \theta_C}{2}\)

⇒ \( 300 = \frac{620 + \theta_C}{2} ⇒ \theta_C = -20^oC\)