Question

The figure given below shows a mercury barometer, with some air trapped in the tube. Atmospheric pressure is given as 101, 000 Pa. Find the pressure of the trapped gas. Given, density of mercury = 13600 kg/m${}^3$.

• A. $P_{air}$ = 37820 Pa
• B. $P_{air}$ = 16965 Pa
• C. $P_{air}$ = 72966 Pa
• D. $P_{air}$ = 27696 Pa

Answer 1

The correct option is D $P_{air}$ = 27696 Pa

Let the pressure of the trapped air be $P_{air}$ and $P_{atm}$ is the atmospheric pressure.

Since, height of the mercury column is 55 cm and the pressure at the mercury surface is equal to atmospheric pressure.
So, we can say
$P_{atm}$ = Pressure of 55 cm height mercury + $P_{air}$
101,000 = $\rho \times g\times 0.55$ + $P_{air}$
$P_{air}$ = 27696 Pa