Question

The thermo emf of a thermocouple varies with temperature as \( E = A\theta + B\theta^2 \). If the cold junction is kept at \( 0^\circ C \), the neutral temperature is:

• A. \( 0^\circ C \)
• B. \( 600^\circ C \)
• C. \( 150^\circ C \)
• D. No neutral temperature is possible

Hint:

For thermocouples, the neutral temperature occurs where the emf becomes zero. For equations with a form \( E = A\theta + B\theta^2 \), no valid neutral temperature exists if \(A\) and \(B\) are arbitrary constants without a specific relationship to yield a positive value for \(\theta\).

Answer 1

The Correct Option is D

The neutral temperature of a thermocouple is the temperature at which the thermo emf (\(E\)) becomes zero. This temperature is important for the calibration and measurement in thermocouples. The given relationship for the thermo emf is: \[ E = A\theta + B\theta^2 \] Where: - \( E \) is the thermo emf, - \( \theta \) is the temperature in Celsius, - \( A \) and \( B \) are constants. To find the neutral temperature, we set the thermo emf \(E = 0\) because at the neutral temperature, the emf is zero. Thus, we solve the equation for \(E = 0\): \[ 0 = A\theta + B\theta^2 \] Factoring the equation: \[ \theta(A + B\theta) = 0 \] This gives two solutions: - \( \theta = 0 \), which represents the cold junction temperature. - \( A + B\theta = 0 \), which gives \( \theta = -\frac{A}{B} \). Now, we see that for the neutral temperature to exist, the value of \( -\frac{A}{B} \) should give a positive temperature. However, in the form \( E = A\theta + B\theta^2 \), there is no condition that guarantees a positive value for \( \theta \) other than zero. Hence, there is no valid neutral temperature for the given equation. Thus, the correct answer is No neutral temperature is possible.