Question

On a very hot day, when the temperature is ${40^0} C$ , what is the proportional correction $\dfrac {{h' - h}} {h} $ that must be applied to the observed column height $h$ of a mercury barometer? Weather services usually quote barometric pressure with a precision of about 1 part in ${10^3} $. Determine whether such a measurement requires further correction for the expansion of the glass barometer tube, at least on very hot days. If it does, is the volume coefficient $\beta $ or the linear coefficient $\alpha $ the appropriate quantity to use in correcting?

Answer 1

Hint: Think of how the mercury barometer would change when the particular height is altered accordingly. Use the relation between $\alpha $ and $\beta $ to determine the further corrections required for expansion of the glass barometer tube.

Complete step by step solution:
A barometer of mercury is an appliance used in a given position to measure the ambient tension. A vertical glass tube is a barometer that is closed at one end. The closed end is on the top and is placed on the bottom of the mercury-filled tub. The pressure gauge is absolute. Broad, hollow and vertical glass tube of mercury evacuates the air. Often known as the Torricellian Barometer are mercury barometers.

It calculates ambient pressure by the mercury tube adjustment to match the atmospheric force on the reservoir by the weight of the mercury sheet. This indicates that the unit displays the air pressure in the height of a mercury column. The measurement of the air pressure is inch or millimetres of mercury, according to the configuration of the mercury barometer. At every degree of the atmosphere, the ambient pressure depends on the overhead air weight. A barometer of mercury can be considered an instrument or an extent determining the weight of the atmosphere above. With a reference to a seesaw the concept of a barometer may be appreciated. The processes and the principle of a mercury barometer can be easily defined by understanding the principle of a See-Saw.

A barometer of mercury is used as a balance. The weight of mercury in the instrument balances the ambient weight at a specific spot. The presence of air on all the measurements cannot calculate the ambient pressure at a balance size. Thus an end is closed in a barometer so that air does not affect scale and calculation. The theory of equalising air pressure with the quantity of mercury found in the instrument is also a Mercury Barometer.

Proportional correction which should be applied to pragmatic column height $h$ of a mercury barometer is,
$\dfrac {{h' - h}} {h} = 0.727\% $
${\alpha _ {glass}} $ is the applicable parameter since the cross -sectional area is extraneous.
\[h\prime \prime = h (1 + {\beta _ {Hg}} t) (1 - {\alpha _{glass}}t)\;.\;\]
since \[{\beta _ {glass}} = 2.6 \times {10^ {- 5}} {K^ {- 1}}\]
\[\alpha = \dfrac{\beta} {3} = 0.9 \times {10^ {- 5}}\]
Even for \[t = {40^0}C\], \[{\alpha _{glass}}t = 3.6 \times {10^{ - 4}}\] which is not adequate to affect the construing to 1 part in ${10^3}$.

Note: Be careful while calculating the coefficients $\alpha $ and $\beta $. Take the appropriate measurements and take the approximation nearest to two decimal places. Also take all the units of required quantities in their respective standard units while calculating the coefficients $\alpha $ and $\beta $.