Question

Cold junction of thermocouple is at $0^{0}C$ and the other junction at $t^{0}C$ if thermo emf is a function of temperature is given by $E=[10\times {10}^{-6}t-\frac{1}{40}\times {10}^{-6}{t}^2]$, maximum value of thermo emf is :

• A. $4$ mV
• B. $3$ mV
• C. $2$ mV
• D. $1$ mV

Answer 1

The correct option is D $1$ mV

Given,
$T_c=0^{o}C$
$T_n=t^{o}C$
Also,
$E={10}^{-5}t+\left(\frac{-{10}^{-6}}{40}\right)t^2$
For maximum thermo EMF,
$\frac{dE}{dt}=0$
$\therefore {10}^{-5}-\frac{{10}^{-6}}{40}\left(2t\right)=0$
$\therefore t=200$
Thus,
$E={10}^{-5}\left(200\right)-\frac{{10}^{-6}}{40}(200{)}^2$
$={10}^{-3}V$
$=1mV$