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No, hot air takes up more space than cold air. When matter is heated, it expands, when it is chilled, it contracts (water is an exception, as ice crystals expand from liquid water). To prove this, take an empty water bottle and shove it in the freezer for an hour or so. When taken out, the air inside the bottle will be cold. If you wrap a balloon around the bottle's opening, you will trap the cold air inside the bottle. Now, pour some hot water over the bottle, heating it, and the air inside (be careful). As the air warms, it will expand, and therefore take up more room. Since the bottle is a confined space, the balloon over the bottle's mouth will inflate slightly to give somewhere for the expanded air to go.

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