One junction of a certain thermoelectric coup | vedclass

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(A) Thermoelectric power $S$ is defined as the rate of change of thermo-electromotive force $E$ with respect to temperature $T$,i.e.,$S = \frac{dE}{dT

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

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(A) Thermoelectric power $S$ is defined as the rate of change of thermo-electromotive force $E$ with respect to temperature $T$,i.e.,$S = \frac{dE}{dT}$.Given the expression for $E$ is $E = k(T - T_r)[T_0 - \frac{1}{2}(T + T_r)]$.Expanding the expression: $E = k[T_0 T - T_0 T_r - \frac{1}{2}T^2 - \frac{1}{2}T T_r + \frac{1}{2}T T_r + \frac{1}{2}T_r^2] = k[T_0 T - T_0 T_r - \frac{1}{2}T^2 + \frac{1}{2}T_r^2]$.Differentiating $E$ with respect to $T$: $\frac{dE}{dT} = k[T_0 - T]$.Substituting the given temperature $T = \frac{1}{2} T_0$ into the expression for $S$:$S = k[T_0 - \frac{1}{2} T_0] = k[\frac{1}{2} T_0] = \frac{1}{2} k T_0$.

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 $E=k(T-T_r)[T_0-\frac{1}{2}(T+T_r)]$. At temperature $T=\frac{1}{2} T_0$,the thermoelectric power is

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