1. For a thermocouple with cold junction at $0^\circ C$, the thermo-emf is given by $E = a\theta + b\theta^2$ where $\theta$ is the temperature of the hot junction.

2. The neutral temperature $\theta_n$ is the temperature at which emf is maximum. So, $\frac{dE}{d\theta} = 0$

3. Differentiate: $\frac{dE}{d\theta} = a + 2b\theta$ Setting this equal to zero: $a + 2b\theta_n = 0$ $\theta_n = -\frac{a}{2b}$

4. Given: $\frac{a}{b} = 700^\circ C$ Hence, $\theta_n = -\frac{1}{2}\cdot \frac{a}{b} = -\frac{700}{2} = -350^\circ C$

5. Since the neutral temperature comes out to be negative, it is not physically attainable here for the hot junction when the cold junction is fixed at $0^\circ C$. Thus, no neutral temperature is possible for this thermocouple in the given situation.

6. Checking options:

• A: $1400^\circ C$ $\rightarrow$ incorrect
• B: $350^\circ C$ $\rightarrow$ incorrect sign
• C: $700^\circ C$ $\rightarrow$ incorrect
• D: No neutral temperature is possible $\rightarrow$ correct

Therefore, the correct answer is D.