What is the effect on the vertical height of the mercury column in a barometer of a) using a wider glass tube, b) pushing the
tube further into the bowl, c) tilting the glass tube at an angle and d) taking the barometer to the top of a mountain?
[ this is a question about the differentiation of barometer in 4 situations, so, please consider that as 1 question]
The height of mercury above the bowl in a barometer is a measure of the pressure of air pushing on the mercury in the bowl. The mass of the mercury above the bowl times the force of gravity is equal to the pressure of air on the bowl. In example A, B, and C the air pressure is constant so you will have the same quantity of mercury in the tube. The question in these three examples is how is this quantity observed. In example:
- In (A) the tube is wider so the height has to be lower
- In (B) the height would not change
- In (C) tilting the tub will not change the height. It will just make it harder to read. Like tilting a bottle of soda, the mercury will tilt in the tube so that the reading on the side closest to the earth will be higher and the side away would be lower.
- In (D) at the top of a mountain the air pressure is much lower so the vertical height will be lower. It should be noted that the force of gravity at the top of a mountain is lower that at sea level so the drop in height will not be as large as one would expect.
Effects of each of the four action on the barometer are discussed below.
a) Using a wider glass tube
Irrespective of the diameter of the barometer glass tube the height of the mercury column in the glass tube above the level of mercury will remain same. This is neglecting the effect of surface tension which, in any case will be negligible with the tube diameters generally used in barometers.
b) Pushing the glass tube further into the bowl
The height of the mercury column in the barometer above the level of mercury in the bowl will remain same irrespective of how deep in the bowl the glass tube is pushed. Of course, if the part of the glass tube above the level of mercury in the bowl is not long enough to accommodate the complete height of the mercury column, the mercury will rise to the top of the tube.
c) Tilting the glass tube at an angle
The vertical height of the mercury in the glass tube remains same irrespective of the angle of tilt of the glass tube. However, it should be noted that length of glass tube occupied by mercury increases with the angle of tilt. This length is minimum when the glass tube is vertical.
d) Taking the barometer to the top of a mountain
The atmospheric pressure at a mountain top will be lower at the mountain top as compared to sea level or at bottom of the hill. Therefore when the barometer is taken to the top of a mountain, the height of mercury column in the glass tube will be less.