Question

For a chromel-constantan (type E) thermocouple, the junction potential E $\left(in\mu V\right)$ at $0^{o}C$ is given by

$E=58.66\theta +4.54\times {10}^{-2}{\theta }^2+2.89\times {10}^{-5}{\theta }^3-3.30\times {10}^{-7}{\theta }^4+\text{higher order terms.}$

Assuming the cold junction compensation. The sensitivity of thermocouple at 100${}^o$C is

• A. $6.31mV{/}^{o}C$
• B. $6.31\mu V{/}^{o}C$
• C. $67.28\mu V{/}^{o}C$
• D. $67.28mV{/}^{o}C$

Answer 1

The correct option is C $67.28\mu V{/}^{o}C$

For the given thermocouple

$E=58.66\theta +4.54\times {10}^{-2}{\theta }^2+2.89\times {10}^{-5}{\theta }^3+3.30\times {10}^{-7}{\theta }^4+higherorderterms$

$Sensitivity,S=\frac{dE}{d\theta }{|}_{\theta ={100}^{o}C}$

$=\frac{d}{d\theta }[58.66\theta +4.54\times {10}^{-2}{\theta }^2+2.89\times {10}^{-5}{\theta }^3+3.30\times {10}^{-7}{\theta }^4]$

$=58.66+4.54\times {10}^{-2}\left(2\theta \right)+2.89\times {10}^{-5}\left(3{\theta }^2\right)+3.30\times {10}^{-7}\left(4{\theta }^3\right)$

$=58.66+4.54\times {10}^{-2}(2\times 100)+2.89\times {10}^{-5}(3\times {100}^2)+3.30\times {10}^{-7}(4\times {100}^3)$

$=58.66+9.08+0.867-1.32$

$=67.28\mu V{/}^{o}C$