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
  1. $\frac{1}{2} k T_0$
  2. $k T_0$
  3. $\frac{1}{2} k T_0^2$
  4. $\frac{1}{2} k\left(T_0-T_r\right)^2$

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 $S=\frac{1}{2} k T_0$

Asked in: AP EAMCET 2008

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