Question

A barometer has become faulty because some air has leaked into the space above the mercury column. The height of the mercury column is $70cm$ and the length of the space above the mercury is $10cm$. The barometer space is pushed further down into the mercury trough. The length of space above mercury reduces to $6cm$ and the height of mercury column is found to decrease to $67cm$. This information shows that the true atmospheric pressure must be:

• A. $74.5cm$ of Hg
• B. $75.0cm$ of Hg
• C. $75.5cm$ of Hg
• D. $76.0cm$ of Hg

Answer 1

Answer: (A)

$V_1$ is volume of air trapped

$V_1$ = A $\times$ 10

$V_2$ is volume of air trapped in 2

$V_2$ = A $\times$ 6

& $P_1=(P_0-70)$ un of Hg

$P_2=(P_0-67)$ un of Hg

So from Boyle's law

$P_1{V}_1=P_2{V}_1$

$(P_0-70)\times 10\times A=(P_0-67)\times 6\times A$

${10P}_0-700=6P_0-6\times 67$

${4P}_0=700-6\times 67$

$P_0=\frac{298}{4}=74.5un.ofHg$