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# Using a total immersion thermometer only partially immersed

When total immersion thermometers are used in a condition wherein the entire liquid column is not exposed to the temperature being measured, a stem correction must be computed and applied to the observed reading to obtain the actual temperature of the liquid being measured.

Example: You have a total immersion mercury thermometer graduated from -1 to 101 °C in 0.1 divisions. You are measuring the temperature of liquid in a beaker on a hot plate; the thermometer is immersed to the 31 degree mark. The reading of the thermometer is 90.15 °C.

How much error do you have for incorrect immersion of the thermometer?

What is the actual temperature of the liquid being measured?

#### 1. We need to determine 4 variables:

k = the coefficient of expansion of the thermometric liquid and the glass, combined.
For Celsius mercury thermometers, k = 0.00016
For Fahrenheit mercury thermometers, k = 0.00009
For red liquid Celsius thermometers, k = 0.001
For red liquid Fahrenheit thermometers, k = 0.0006

n = the number of scale degrees of the thermometer column between the surface of the liquid being measured and the meniscus of the liquid column.
In this example, the thermometer is immersed to to 31 degree mark, and the reading of the thermometer is 90.15, so the value of N is 90.15 minus 31, or 60.15 (the distance, expressed in scale degrees between the 31 graduation at the surface of the liquid in the beaker and the meniscus at 90.15).

T = the reading of the thermometer in situ
(In this example, 90.15 °C)

t = average temperature of the emergent liquid column.
To obtain this value, suspend alongside the main thermometer a secondary, total immersion thermometer. Position this thermometer so that its bulb is centered halfway between the surface of the liquid and the temperature indicated on the main thermometer. The temperature indicated on the second thermometer will be the average temperature of the emergent liquid column. For this example, we will assume a temperature of 25 °C was observed.

#### 2. Now, find the magnitude of the correction from the following equation:

correction = kn(T-t)

(0.00016 x 60.15) x (90.15-25) = 0.627

Adding this value to the observed reading of the thermometer yields 90.15° + .627 = 90.777 °C which is the actual temperature of the liquid being measured.

If this were a red liquid filled thermometer, you would need to use a different value for k (above). Notice how much greater the correction is:

(0.001 x 60.15) x (90.15-25) = 3.918

Adding this value to the observed reading of the thermometer yields 90.15° + 3.918° = 94.068 °C which is the actual temperature of the liquid being measured.

Caution: although this equation (from ASTM E-77and NBS Monograph 150) is reasonably accurate, the measurement of the temperature of the emergent stem is difficult and often imprecise, and will increase the measurement uncertainty.

Remember that the greater the departure of the test temperature from room temperature, the greater the correction – and the greater the uncertainty of the measurement.

The ideal situation is to use the correct thermometer for your application, and not try to ‘make do’ with what you have at hand.

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