My Chem lab professor said that we have to wait for things to cool to room temperature so we could get an accurate measurement. I don't understand why.
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There's two reasons why you have to wait for a constant temperature to weigh something: one is that hot air is less dense than cold air, and can produce a buoyancy that tends to lift the object up and reduce its weight. Also, if you are heating something to dry it out, water molecules will be released from the sample, changing the weight. You want to heat something enough to remove the water, and then wait for it to cool to room temperature to weigh.
In addition, I would assume that there's the underlying motive of teaching repeatability and protocol. If you weigh something while it's cooling down, you don't know what the temperature is. If the temperature does end up affecting the data, you won't be able to account for it. If you let it cool to room temperature each time, then it's more consistent and leaves less room for variation.
You have to weigh them at a reference temperature so that you can also get their volume at the same temperature, and thus determine their density at that temperature.
They weigh the same amount, he's wrong.
Changing the temperature of something only changes the weight if it adds things from or looses things to the atmosphere, eg a hot glass weighs slightly less than a cold glass because there is a thin film of water on all glass surfaces at room temperature.
what is more likely is that the scales are not meant to handle hot things and the temperature will upset the mechanism it uses to determine the weight (eg if it uses a spring the spring will soften when heated)
while I think the above explanations also have good elements to them, I think your last element is probably the key to this.
The lab equipment can warp and become damaged when exposed to high temperatures. This equipment needs to be sensitive enough to accurately measure things like weight, and so is somewhat delicate.
In addition, a hot object will always weigh more than a cold object, even if the two objects are otherwise identical in every way, although the difference is incredibly small, and far beyond your ability to measure.
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