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# Using a partial immersion thermometer in condition of total immersion

Suppose you have an ASTM 91C thermometer, with a range of +20 to 50 °C in 0.1 divisions, 76mm immersion, and you want to place the thermometer inside an incubator (in condition of total immersion) and read the temperature. Do you have to make a correction? Yes.

#### 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 immersion mark on the thermometer and the meniscus of the liquid column.
The ungraduated portion of the thermometer between the immersion line and the start of the scale (if any) must be evaluated and included in the value of n. This concept is a little more difficult. Suppose on this thermometer the scale starts (the first graduation is at 20 °C) 25mm above the immersion line. The thermometer in situ reads 37.12 °C The value of n, therefore is the number of scale degrees between 20° and 37.12 °C (17.12) plus the number of degrees represented by the 25mm of ungraduated capillary. Using a metric ruler, place the 0 on the ruler at 20 °C on the thermometer. What temperature on the thermometer coincides with 25 on the ruler? Let’s say 23.8 °C. So, 25mm equals the span from 20 to 23.8, or 3.8 degrees. Add the 3.8 thus determined to the 17.12 we figured above, and we find that n = 20.92

to = the reading of the thermometer in situ
(In this example, 37.12 °C)

ts = The specified temperature of the emergent liquid column, from ASTM E-1 ‘Specifications for ASTM Thermometers’.
This particular thermometer was manufactured anticipating an emergent stem temperature of 25 °C at all temperatures, so use this value for ts Thumbnail rule: if your thermometer is NOT to be an ASTM thermometer, use 23 °C as the value of ts.

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

Magnitude of the correction = kn(ts – to)

(0.00016 x 20.92) x (25-37.12) = -0.04 °C

Add this value (algebraically) to the observed temperature to find the actual temperature in the incubator:

37.12° + (-0.04°) = 37.08 °C

Remember that the greater the departure of the test temperature from the specified stem 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.