At the middle of the mercury barometer tube there is a little column of air with the length lo and there is vacuum at the top as shown. Under the normal atmospheric pressure and the temperature of 300 kelvin, l0 = 10cm  Neglect expansion of the tube. The length of the air column if the temperature rises to 330 kelvin in equilibrium will be

Pressure in the air inside the column of mercury is equal to the weight of mercury over the air divided by the internal cross sectional area of the tube. When the  temperature increases, the weight of the upper part of the mercury column does not change. That is why the pressure in the air is also constant. For the isobaric process, the change in volume is proportional to the change in temperature. The same is true for the lengths of the air column.