One junction of a certain thermoelectric couple is at a fixed temperature $T_r$ and the other junction is at…
One junction of a certain thermoelectric couple is at a fixed temperature $T_r$ and the other junction is at temperature $T$. The thermo-electromotive force for this is
expressed by $E=k\left(T-T_r\right)\left[T_0-\frac{1}{2}\left(T+T_r\right)\right]$. At temperature $T=\frac{1}{2} T_0$, the thermoelectric power is
$\frac{1}{2} k T_0$
$k T_0$
$\frac{1}{2} k T_0^2$
$\frac{1}{2} k\left(T_0-T_r\right)^2$
Solution
We know that thermoelectric power
$
S=\frac{d E}{d T}
$
Given, $E=K\left(T-T_r\right)\left[T_0-\frac{1}{2}\left(T+T_r\right)\right]$
By differentiating the above equation w.r.t. $T$ and putting $T=\frac{1}{2} T_0$, we get $S=\frac{1}{2} k T_0$