Question

In a thermocouple, the neutral temperature is $$270^\circ \,C$$ and the temperature of inversion is $525^\circ C$. The temperature of the cold junction would be
A. $30^\circ \,C$
B. $255^\circ \,C$
C. $15^\circ \,C$
D. $25^\circ \,C$

Answer 1

Hint: A thermocouple is defined as a sensor that is used for measuring the temperature. A thermocouple consists of two dissimilar wires, in which one wire is connected to the sensor and the other wire is connected to the thermometer. Here, to calculate the temperature of the cold junction we will use the formula, which is shown below.

Formula used:
Now, the formula used for calculating the cold junction is given by
 ${T_n} = \dfrac{{{T_i} + {T_c}}}{2}$
Here, ${T_n}$ is the neutral temperature, ${T_i}$ is the temperature of inversion and ${T_c}$ is the temperature of a cold junction.

Complete step by step answer:
In the question, neutral temperature and temperature of inversion is given.
Neutral temperature is defined as the temperature of the hot junction at which the thermo-emf will become maximum and is given by
${T_n} = 270^\circ \,C$
On the other hand, temperature of inversion is the temperature at which the emf will change its sign, that is, the current will be in reverse direction and is given by
${T_i} = 525^\circ \,C$
Now, the formula used for calculating the temperature of the cold junction is given by
 ${T_n} = \dfrac{{{T_i} + {T_c}}}{2}$
$ \Rightarrow \,2{T_n} = {T_i} + {T_c}$
$ \Rightarrow \,{T_c} = 2{T_n} - {T_i}$
Putting the values of neutral and inversion temperature, we get
$ \Rightarrow \,{T_c} = 2\left( {270} \right) - 525$
$ \Rightarrow \,{T_c} = 540 - 525$
$ \therefore\,{T_c} = 15^\circ C$
Therefore, the temperature of the cold junction is $15^\circ C$.

Hence, option C is the correct option.

Note:The thermocouple will work on the principle based on three effects that are Seebeck effect, Peltier effect and Thomson effect. When the temperature of the cold junction will be $0^\circ C$ , the temperature of the hot junction will increase. Therefore, in the above solution we got the temperature of the cold junction as $15^\circ C$ which means the temperature of the hot junction will be less.