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Nernst Equation

One junction ...

Question

One junction of a certain thermocouple is at a fixed temperature $T_{r}$ and the other junction is at a temperature T. The electormotive force for this is expressed by,
$E = K (T - T_{r}) [T_{0} - \frac{1}{2} (T + T_{r})]$
At temperature T = $T_{0} / 2$ , the thermo electric power is

k T_{0} / 2

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k T_{0}

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\frac{k T_{0}^{2}}{2}

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\frac{1}{2} k (T_{0} - T_{i})^{2}

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Solution

The correct option is A $k T_{0} / 2$
Given, $E = k (T - T_{r}) [T_{0} - \frac{1}{2} (T + T_{r})]$
Thermoelectric power, $\frac{d E}{d T} = k (T - T_{r}) [- \frac{1}{2}] + [T_{0} - \frac{1}{2} (T + T_{r})] (k)$ (differentiate using by parts)
or $\frac{d E}{d T} = k [- T / 2 + T_{r} / 2 + T_{0} - T / 2 - T_{r} / 2] = k [T_{0} - T]$
At $T = T_{0} / 2, \frac{d E}{d T} = k [T_{0} - T_{0} / 2] = k T_{0} / 2$

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