First slide

Thermometry

Question

The thermo e.m.f. of a thermocouple varies with the temperature $θ$ of the hot junction as $E = aθ - {bθ}^{2} volt$ where the ratio (a / b) is 700°C. If the cold junction is kept at 0°C, then the neutral temperature is

Easy

A

700°C
B

350°C
C

1400°C
D

no neutral temperature is possible

Solution

Given that, E $= aθ - {bθ}^{2}$
$∴ \frac{dE}{dθ} = a - 2 bθ$
neutral temperature $θ_{n} = \frac{dE}{dθ} = 0$
$∴ a - 2 {bθ}_{n} = 0 or θ_{n} = (a / 2 b)^{\circ} C$
$∴ θ_{n} = \frac{700}{2} = 350^{\circ} C$

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