Question

barometer reads 75 cm of mercury. When $2.0 \,cm^3$ of air at atmospheric pressure is introduced into the space above the mercury level, the volume of this space becomes $50 \,cm^3$. The length by which the mercury column descends is

• A. 3 cm of Hg
• B. 7 cm of Hg
• C. 30 cm of Hg
• D. 10 cm of Hg

Answer 1

Answer: (A)

3 cm of Hg

Answer 2

initially barometer reads $75 cm$, so atmosphere pressure $P _{ a }=\rho g(0.75)$ gas is added at atmosphere pressure, with initial volume $2 cc$ later volume expands to $50 c c$. This is isothermal process, by boyle's law $P _{2} V _{2}= P _{1} V _{1}$ $P _{2}=\frac{ P _{1} V _{1}}{ V _{2}}$ since $P _{1}= P _{ a }$ $\begin{array}{l} P _{2}=\frac{\rho g(0.75) \times 2}{50} \\\ P _{2}=\rho g(0.03) \end{array}$ applying hydro-static pressure equation(as shown in image) $\begin{array}{l} P _{2}+\rho g h = P _{ a } \\\ \rho g(0.03)+\rho g h=\rho g(0.75) \\\ h =0.72 m =72 cm \end{array}$ descend in mercury column is $=75-72=3 cm$