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 18 g, of which 4.5 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).

Answer 1

-Qout=Qin
---------
-(Qwater+Qvial)=Qthermometer+Qmercury
-(mwater*cwater*(Tfinal-Tinitial)+mvial*cvial*(Tfinal-Tinitial)) = mthermometer*cthermometer*(Tfinal-Tinitial)+mmercury*cmercury*(Tfinal-Tinitial)

Plug in the equilibrium temperature for Tfinal. Then plug in the Room temperature for Thermometer and Mercury Tinitial. Solve for Water and Vial Tinitial. Done.

Make sure to use the right C numbers if you change the masses to kg.