When an immersion glass thermometer is used to measure the temperature of a liqu

Question

When an immersion glass thermometer is used to measure the temperature of a liquid, the temperature reading will be affected by an error due to heat transfer between the liquid and the thermometer. Suppose you want to measure the temperature of 7 mL of water in a Pyrex glass vial thermally insulated from the environment. The empty vial has a mass of 5.0 g. The thermometer you use is made of Pyrex glass as well and has a mass of 17 g, of which 6.6 g is the mercury inside the thermometer. The thermometer is initially at room temperature (20.0°C). You place the thermometer in the water in the vial and, after a while, you read an equilibrium temperature of 29°C. What was the actual temperature of the water in the vial before the temperature was measured? The specific heat capacity of Pyrex glass around room temperature is 800 J/(kg K) and that of liquid mercury at room temperature is 140 J/(kg K).

Explanation / Answer

The vial-water system has a heat capacity of Cw = 7*4.18 + 5*.8 J/K, and the thermometer has a heat capacity of CT = 10.4*.8 + .14*6.6 J/K. The thermometer absorbs 9*CT, which came from the water. The initial temperature of the water is then 29 C + (9*CT)/Cw =29 + 9(10.4*.8 + .14*6.6)/(7*4.18 + 5*.8)= 31.5° C.

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