Question

The temperature of the cold junction of the thermocouple is ${{0}^{0}}C$ and the temperature of the hot junction is ${{T}^{0}}C$. The emf is $E=16T-0.04{{T}^{2}}$ in microvolts. The inversion temperature ${{T}_{i}}$ is?
A. ${{300}^{0}}C$
B. ${{200}^{0}}C$
C. ${{500}^{0}}C$
D. ${{400}^{0}}C$

Answer 1

Hint:The inversion temperature is defined as that temperature of the body at which thermo emf becomes zero. In other words, we can say that the temperature at which thermo emf changes its sign. For thermocouple emf value is zero at the hotter section. The temperature can be measured either in degree Celsius or degree Kelvins.

Complete step by step answer:
At inversion temperature, $E=0$, thus,
$E=16T-0.04{{T}^{2}}$
$\Rightarrow 0=16T-0.04{{T}^{2}}$
$\Rightarrow 16-0.04{{T}_{i}}=0$
$\Rightarrow 0.04{{T}_{i}}=16$
$\therefore{{T}_{i}}={{400}^{0}}C$
So, the inversion temperature comes out to be 400 $^{0}C$.

So, the correct option is D.

Additional Information:
While solving problems in physics in thermodynamics we are often faced with the dilemma of which scale we have to keep the temperature. Usually in the question the data is provided in Celsius scale, but while solving thermodynamics problems it is always an advantage to change all the temperature into Kelvin.

Note:There are different temperature scales which are used as per the feasibility. There is a scale called absolute scale & in that scale the initial point starts from zero and it moves only in one direction. Thus, in such scales, we cannot measure temperature lower than zero. Important temperature scales used widely are Kelvin scale, Celsius scale etc. The lowest temperature that can be recorded in Celsius scale is -273.15 \[{}^\circ C\]contrary to this the lowest temperature that can be recorded In the Kelvin scale is 0$^{0}C$.