13 Jul 2026

Calibration of a Thermocouple and Unknown Temperature

practical ug-v thermal-physics thermocouple calibration

Aim

To calibrate a thermocouple against a standard thermometer and determine an unknown temperature.

Apparatus

Thermocouple, standard thermometer, constant-temperature baths, millivoltmeter, and heating arrangement.

Theory

For a fixed reference junction, the thermo-emf is calibrated against known temperatures. The calibration relation in the working range is approximated by

\[E=a+bT.\]

The unknown temperature is obtained by substituting the measured emf in this equation.

Observations

Standard temperature (°C)	Thermo-emf (mV)
20	0.00
40	0.43
60	0.81
80	1.15
100	1.44

Calibration graph

Thermo-emf plotted against the standard temperature.

Unknown emf: $E=0.96\,\text{mV}$.

Calculation

From the calibration graph, $E=0.96\,\text{mV}$ corresponds to

\[\boxed{T=68^\circ\text{C}}.\]

Result

The temperature of the unknown bath is $68^\circ\text{C}$.

Precautions

1. Keep the reference junction at a fixed temperature.
2. Wait for both junctions to reach thermal equilibrium.
3. Do not immerse the electrical joints in the bath.

Viva Questions

1. Why is calibration needed? Thermo-emf depends on the metal pair and the reference temperature.
2. What is interpolation? It is estimating a value between two calibrated readings.
3. Why should the reference junction be fixed? Otherwise the emf would depend on two changing temperatures.

Maxima Code

Download the Maxima calculation file.