The e.m.f of Cu-Fe thermocouple varies with temperature of hot junction as given by e.m.f (in mv)=14x-0.02x^2.calculate the inversion and neutral temperature?

To find the inversion temperature, we need to find the maximum or minimum point of the function. This can be done by taking the derivative of the function and setting it equal to zero.

Given e.m.f (in mV) = 14x - 0.02x^2

Taking the derivative of the function with respect to x:

d(e.m.f)/dx = 14 - 0.04x

Setting the derivative equal to zero:

14 - 0.04x = 0
0.04x = 14
x = 350

Therefore, the inversion temperature is 350°C.

To find the neutral temperature, we need to find the point where the e.m.f is zero. This can be done by setting the function equal to zero and solving for x.

14x - 0.02x^2 = 0
x(14 - 0.02x) = 0
x = 0 or x = 700

Therefore, the neutral temperature is 0°C or 700°C.

The inversion temperature is the temperature at which the e.m.f. of the thermocouple changes sign. To find the inversion temperature, we set e.m.f. = 0 and solve for x:

```
14x - 0.02x^2 = 0
x(14 - 0.02x) = 0
x = 0 or x = 700
```

So the inversion temperature is 700°C.

The neutral temperature is the temperature at which the e.m.f. of the thermocouple is zero. To find the neutral temperature, we again set e.m.f. = 0 and solve for x:

```
14x - 0.02x^2 = 0
x(14 - 0.02x) = 0
x = 0 or x = 700
```

So the neutral temperature is also 700°C.