The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as $E=a\theta+b\theta^{2}$ 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

(D) no neutral temperature is possible for this thermocouple.

JEE Main · 2004 · 24 Apr 2004 · Offline · Chapter_pending

The thermo emf of a thermocouple varies with the temperature

θ

of the hot junction as

E = a θ + b θ^{2}

in volts where the ratio

a / b

70 0^{\circ} C

. If the cold junction is kept at

0^{\circ} C

, then the neutral temperature is

Answer: (D)

The thermo emf is

E = a θ + b θ^{2}

, and the neutral temperature is the point where the emf stops rising,

\frac{d E}{d θ} = a + 2 b θ_{n} = 0

, so

θ_{n} = - \frac{a}{2 b}

. With

\frac{a}{b} = 70 0^{\circ}

C this gives

θ_{n} = - 35 0^{\circ}

C. A neutral temperature lying below the cold junction at

0^{\circ}

C has no physical meaning, so for this thermocouple no neutral temperature is possible.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option