A

Step 1: Understand the scenario: The mercury expands when heated, leading to a change in volume. The expansion of the mercury can be expressed using the coefficient of volume expansion.
Step 2: Calculate the change in volume of mercury due to the temperature change. The formula for volume expansion is given by:
$$ \Delta V = V_0 \beta \Delta T $$
where:
$$ \Delta V $$ = change in volume,
$$ V_0 $$ = initial volume,
$$ \beta $$ = coefficient of volume expansion (0.00018 per ºC),
$$ \Delta T $$ = change in temperature (1ºC).
Step 3: The increase in volume will cause a rise in the height of the mercury column. However, since the barometer is in a vacuum, this rise is countered by the atmospheric pressure acting on the mercury surface.
Step 4: Since the tube is very narrow and the increase in mercury height is negligible due to the volume increase being completely balanced by atmospheric pressure, the height of mercury remains unchanged.
Therefore, A.