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The way a thermometer works is that mercury expands when it absorbs heat. This absorption of heat is responsible for mercury rising in a thermometer under warm conditions. Since energy can still be transferred, it is considered a closed system rather than an isolated one.
If a thermometer was an isolated system, it would not be able to interact with its surroundings, aka the mercury in the thermometer would not rise or fall according to different temperatures. Thus, we can rule out that a thermometer is an isolated system just on the principle that it works. Additionally, since the mercury is in a closed tube, we know that this must be a closed system as it is not open to its surroundings.
It's really easy to confuse isolated and closed systems but the key in this example is to recognize that the mercury is affected by the temperature outside, so there there is an exchange of energy in the form of heat between the contents of the system (mercury) and the surroundings.
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