The thermo emf of a hypothetical thermocouple varies with the temperature θ of hot junction as E=a θ+b θ2 in volts, where the ratio a / b is 700° C. If the cold junction is kept at 0° C, then the neutral temperature is

Question

The thermo emf of a hypothetical thermocouple varies with the temperature θ of hot junction as E=a θ+b θ2 in volts, where the ratio a / b is 700° C. If the cold junction is kept at 0° C, then the neutral temperature is (A) 700° C (B) 1400° C (C) -350° C (D) no neutral temperature is possible for this thermocouple

Tardigrade Admin · Accepted Answer

Given, E=a θ+b θ2 ∴ p =(d E/d θ)=(d/d θ)(a θ+b θ2) =a+2 b θ At θ =Tn, p=0 ⇒ Tn =-(a/2 b)=-350° C

Q. The thermo emf of a hypothetical thermocouple varies with the temperature $θ$ of hot junction as $E = a θ + b θ^{2}$ in volts, where the ratio $a / b$ is $70 0^{\circ} C$ . If the cold junction is kept at $0^{\circ} C$ , then the neutral temperature is

$70 0^{\circ} C$

$140 0^{\circ} C$

$- 35 0^{\circ} C$

no neutral temperature is possible for this thermocouple

Given, $E = a θ + b θ^{2}$
$∴ p = \frac{d E}{d θ} = \frac{d}{d θ} (a θ + b θ^{2})$
$= a + 2 b θ$
At $θ = T_{n}, p = 0$
$\Rightarrow T_{n} = - \frac{a}{2 b} = - 35 0^{\circ} C$

Q. The thermo emf of a hypothetical thermocouple varies with the temperature θ of hot junction as E=aθ+bθ2 in volts, where the ratio a/b is 700∘C. If the cold junction is kept at 0∘C, then the neutral temperature is

700∘C

1400∘C

−350∘C