Is neutral temperature always the arithmetic mean of the inversion temperature and the temperature of the cold junction? Does the unit of temperature have an effect in deciding this question?
No, the neutral cannot be the arithmetic mean of the inversion temperature and the temperature of the cold junction always.
Neutral temperature is defined as the temperature of the hot junction of a thermocouple attains its maximum value, when the clod junction is maintained at a constant temperature of 0oC.
While the inversion temperature is the critical temperature at which a non-ideal gas experiences a decrease in temperature will experience a temperature decrease and above which will experience a temperature increase.
Neutral temperature does not change for a metal whether the temperature of cold junction and inversion temperature change by any value.
This is valid only Celsius is the unit for both the temperatures.