How much higher will mercury stand in the open arm in a J-Tube manometer, if air column in the closed arm is reduced to 4 cm, the mercury id at the same level in both open and closed arms when the air column in the closed arm is 15 cm long. Assume barometric pressure, 1 atm.
To answer this question, we need to understand the principles behind a J-Tube manometer and how it works.
A J-Tube manometer is a device used to measure the pressure of a gas in a closed container. It consists of a U-shaped tube partially filled with mercury, with one arm open to the atmosphere (the open arm) and the other arm connected to the closed container (the closed arm).
In this case, we are given that the air column in the closed arm is reduced to 4 cm, and when the air column is 15 cm, the mercury is at the same level in both the open and closed arms.
To determine the difference in mercury level between the two arms when the air column is 4 cm long, we can use the principle of pressure equilibrium:
The pressure in the open arm (P1) is equal to the atmospheric pressure, which is 1 atm.
The pressure in the closed arm (P2) can be calculated using the formula:
P2 = P1 + ρgh
Where:
P2 is the pressure in the closed arm,
P1 is the pressure in the open arm (1 atm),
ρ is the density of mercury (13,595 kg/m^3), and
g is the acceleration due to gravity (9.8 m/s^2).
h is the difference in mercury level between the two arms.
We know that when the air column in the closed arm is 15 cm long, the mercury levels in both arms are the same. This means that the pressure in the closed arm (P2) is also equal to 1 atm.
Using the formula, we can set up the following equation:
P2 = P1 + ρgh
1 atm = 1 atm + (13,595 kg/m^3) * (9.8 m/s^2) * h
Simplifying the equation:
h = (1 atm - 1 atm) / ((13,595 kg/m^3) * (9.8 m/s^2))
h = 0 / (13344.1 Pa)
h = 0 m
Since h = 0, we can conclude that when the air column in the closed arm is 4 cm long, the mercury level in the open arm will remain the same. Therefore, the mercury will not stand higher in the open arm.
Please note that this calculation assumes idealized conditions and may vary in real-world scenarios due to factors such as temperature and other environmental variables.