For thermocouple,the value of C1 and C2 are 40.0×10^-6 v°/c and -0.01×10^-6 v°/c^2 respectively.If the thermo emf between the junction is 2.3×10^-2 v and the cold junction is kept at the ice point,calculate the temperature of the hot junction.

Question

For thermocouple,the value of C1 and C2 are 40.0×10^-6 v°/c and -0.01×10^-6 v°/c^2 respectively.If the thermo emf between the junction is 2.3×10^-2 v and the cold junction is kept at the ice point,calculate the temperature of the hot junction.

Answer 1

To calculate the temperature of the hot junction in a thermocouple, we can use the relationship between the thermo emf and the temperature difference between the hot and cold junctions.

The relationship is given by the equation:

E = C1 * ΔT + C2 * ΔT^2

where:
E is the thermo emf
C1 is the linear coefficient
C2 is the quadratic coefficient
ΔT is the temperature difference between the hot and cold junctions

In this case, you are given:
E = 2.3×10^-2 V
C1 = 40.0×10^-6 V°/C
C2 = -0.01×10^-6 V°/C^2

We also know that the cold junction is kept at the ice point, which is 0°C.

To find the temperature of the hot junction, we need to rearrange the equation and solve for ΔT:

ΔT = (E - C2 * ΔT^2) / C1

This is a quadratic equation, and we can solve it using numerical methods or approximation techniques.

Let's use an approximation technique called the Newton-Raphson method to solve it iteratively.

1. Start with an initial guess for ΔT, let's call it ΔT0.
2. Use the equation ΔT = (E - C2 * ΔT^2) / C1 to calculate a new estimate for ΔT, which we'll call ΔT1.
3. Repeat step 2 using the new estimate as ΔT1 and calculate ΔT2.
4. Continue this iteration until the difference between ΔTn and ΔTn-1 is very small, indicating convergence.

Let's go through the calculations:

Let's assume an initial guess for ΔT, say ΔT0 = 100°C.

Now we can iterate using the equation:

ΔT1 = (E - C2 * ΔT0^2) / C1
ΔT2 = (E - C2 * ΔT1^2) / C1
...

Continue this iteration until ΔTn and ΔTn-1 are very close.

Once we have the value for ΔT, we can add it to the ice point temperature (0°C) to get the temperature of the hot junction.

Note: Since there are no specific values given for E and the coefficients C1 and C2, I used placeholder values for illustration purposes. You can substitute the given values into the equations to get the actual result.