Q. 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 $E = k\left( T - T_{r} \right)\ \left\lbrack T_{0} - \frac{1}{2}\ \left( T + T_{r} \right) \right\rbrack.$ At temperature $T = \frac{1}{2}\ T_{0},\ $ the thermoelectric power is
A) $\frac{1}{2}kT_{0}$
B) $kT_{0}$
C) $\frac{1}{2}kT_{0}^{2}$
D) $\frac{1}{2}k\ \left( T_{0} - T_{r} \right)^{2}\ $
Explanation
(a) We know that thermoelectric power
$S = \frac{dE}{dT}$
Given, $E = K\left( T - T_{r} \right)\left\lbrack T_{0} - \frac{1}{2}\left( T + T_{r} \right) \right\rbrack$
By differentiating the above equation w.r.t. $T$ and putting $T = \frac{1}{2}\ T_{0},\ $we get $S = \frac{1}{2}kT_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.