Does the temperature of the mercury affects the height of the mercury column in a barometer?
Yes, it does. Mercury is subject to thermal expansion and its vapor pressure varies with temperature.
The vapor pressure is less 0.01 mm Hg below 320 C; this would not be measurable.
The thermal expansion coefficient of mercury is 0.0002 per degree. You can calculate yourself the temperature change needed to get en error of one mm Hg.
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