Question

A thermocouple can be considerd as a single capacity system with a time constant of 100 ms and unity gain. It is immersed in a heat bath whose temperature is varying at $1^{o}C/sfrom{0}^{o}C$ . When the actual temperature of the heat bath is 70 ${}^{o}C$ , the reading of the thermocouple will be

• A. 70.1${}^{o}C$
• B. 71${}^{o}C$
• C. 69.9${}^{o}C$
• D. 69${}^{o}C$

Answer 1

The correct option is C 69.9${}^{o}C$

Error is measurment when a ramp of magnitude 'k' is applied is
$e_{ss}$ = k$\tau$
where, $\tau$ = time constant

$e_{ss}=1\frac{{}^{o}C}{sec}\times 100\times {10}^{-3}sec={0.1}^{o}C$
$\therefore$ the reading of the thermocouple will be
= ${70}^o-{0.1}^{o}C={69.9}^{o}C$