Question

Keeping the cold junction at $0^{0}C$ when hot junction is at ${50}^{0}C$ the thermo emf is 2 mV and when hot junction is at ${100}^{0}C$ thermo emf is 3.5 mV. Neutral temperature of that thermocouple (thermo emf varies as $e=at+b{t}^2$)

• A. ${75}^{0}C$
• B. ${25}^{0}C$
• C. ${50}^{0}C$
• D. ${225}^{0}C$

Answer 1

The correct option is D ${225}^{0}C$

As $e=at+b{t}^2$.

at $t={50}^{o}C,e=2\times {10}^{-3}$.

So $2\times {10}^{-3}=50a+2500b-\left(1\right)$

Similarly, at $t={100}^{o}C,e=3.5\times {10}^{-3}$.

So $3.5\times {10}^{-3}=100a+10000b-\left(2\right)$

From $\left(1\right)and\left(2\right)$,

$a=4.5\times {10}^{-5}$ and $b=-1\times {10}^{-7}$

At neutral temperature, thermo-emf is maximum, so its derivative with respect to temperature is zero at neutral emf.

So $de/dt=a+2bt=0\Rightarrow t=-a/2b=-4.5\times {10}^{-5}/(2\times -1\times {10}^{-7})=450/2={225}^{o}C$

So neutral temperature is ${225}^{o}C$.