Determination of the atmospheric pressure using the quill tube

• $h$: vertical height from the table to the top end of the tube
• $l$: length of air column
• $L$: length of the tube
• $A$: Internal area of cross-section of the tube
• $x$: length of the mercury thread
• $\rho$: density of mercury
• $H$: atmospheric pressure (cm Hg)

According to Boyle's law: $p=\frac{k}{v}$

$$(H + x \sin\theta)\rho g = \frac{k}{Al}$$ $$(H+\frac{xh}{L})\rho~g=\frac{k}{Al}$$ $$\frac{1}{l}=(\frac{Ax~\rho~g}{kL})h+\frac{AH\rho~g}{k}$$

Gradient of the graph of $\frac{1}{l}$ against $h$:

$$H=\frac{Intercept}{Gradient}\times\frac{x}{L}$$ $$\text{Intercept } c = \frac{AH\rho g}{k}$$

1. Attach the tube to the stand as shown in the Figure 22.1 with its closed end on the table and inclined to the horizontal.
2. Measure the height $h$ from the table to the top end of the tube and the length $l$ of the air column and note down these values.
3. Change the inclination of the tube by adjusting the stand and obtain six pairs of values of $h$ and $l$.
4. Also measure and note down the length $x$ of the mercury thread and the length $L$ of the tube.
5. Plot $\frac{1}{l}$ against $h$, calculate the gradient of the graph, obtain the intercept and calculate the atmospheric pressure $H$ as explained in the theory.