Question

The thermo emf of a thermocouple varies with the temperature $θ$ of the hot junction as $E = a \,θ + bθ^2$ in volts where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$, then the neutral temperature is

• A. $700^{\circ}C$
• B. $350^{\circ}C$
• C. $1400^{\circ}C$
• D. no neutral temperature is possible for this thermocouple.

Answer 1

Answer: (D)

$E = aθ + bθ^2$
At neutral temperature $dE/dθ = 0$
$\therefore \frac{dE}{d\theta} = a +2b\theta_{n} = 0 \,;\,\theta_{n}= -\frac{a}{2b}$
Now $\frac{a}{b} = 700^{\circ}C$ (given)
$\theta_{n} =−700/2 = −350^{\circ}C $
Now $θ_{c} = 0^{\circ}C$.
So, $θ_{n} > 0^{\circ}C$
But mathematically $θ_{n} < 0^{\circ }C.$