One junction of a thermocouple is kept at a c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The thermoelectric power $S$ is defined as the rate of change of thermo-emf with respect to temperature,given by $S = \frac{dE}{dT}$.Given the exp

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The thermoelectric power $S$ is defined as the rate of change of thermo-emf with respect to temperature,given by $S = \frac{dE}{dT}$.Given the expression for emf: $E = K(T - T_r) [T_0 - \frac{1}{2}(T + T_r)]$.Let $x = (T - T_r)$. Then $T = x + T_r$. Substituting this into the expression:$E = Kx [T_0 - \frac{1}{2}(x + T_r + T_r)] = Kx [T_0 - \frac{1}{2}(x + 2T_r)] = Kx [T_0 - \frac{1}{2}x - T_r] = K [x(T_0 - T_r) - \frac{1}{2}x^2]$.Differentiating with respect to $T$ (noting $\frac{dx}{dT} = 1$):$\frac{dE}{dT} = K [(T_0 - T_r) - x] = K [T_0 - T_r - (T - T_r)] = K(T_0 - T)$.At $T = \frac{1}{2}T_0$:$S = K(T_0 - \frac{1}{2}T_0) = K(\frac{1}{2}T_0) = \frac{1}{2} K T_0$.

One junction of a thermocouple is kept at a constant temperature $T_r$ and the other junction is kept at a temperature $T$. If the thermo-emf is given by $E = K(T - T_r) [T_0 - \frac{1}{2}(T + T_r)]$,what is the thermoelectric power at $T = \frac{1}{2}T_0$?

Similar Questions

The supply voltage to a room is $120\ V$. The resistance of the lead wires is $6\,\Omega$. $A$ $60\ W$ bulb is already switched on. What is the decrease in voltage across the bulb when a $240\ W$ heater is switched on in parallel to the bulb? ............. $V$

The thermoelectric electromotive force $e$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$. If the temperature of the cold junction is $0 \, ^\circ C$,find the temperature of inversion $t_i$. (Given: $\alpha = 500.0 \, \mu V/^\circ C$,$\beta = 5.0 \, \mu V/^\circ C^2$)

For a given thermocouple,the thermo $e.m.f.$ can be

Two bulbs rated $(25\, W - 220\, V)$ and $(100\, W - 220\, V)$ are connected in series to a $440\, V$ line. Which one is likely to fuse?

$A$ certain amount of charge produces $0.8 \, g$ of $O_2$. How many grams of silver will the same amount of charge produce?

Vedclass Test Series

Exam Paper Generator

Online Exam Module