An oil whose density is 0.775g/mL was used in a open-end manometer to measure the pressure of a gas in a flask, as shown in figure (b). If the height of the oil column is 7.68cm and Pbar = 760.0mmHg. What is the pressure of the gas in the flask in mmHg?
http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
To solve this problem, we need to use the information provided and apply the principles of fluid pressure.
First, let's understand the setup of the manometer. We have an open-end manometer, which means one end of the manometer is open to the atmosphere (Pbar), while the other end is connected to the flask containing the gas.
Now, let's consider the pressures involved in the manometer setup:
1. The pressure of the gas in the flask (Pg) is what we want to find.
2. The pressure exerted by the oil column (Poil) can be determined using the density and height of the oil column.
3. The atmospheric pressure (Pbar) is given as 760.0 mmHg.
We can calculate Poil as follows:
Poil = density x g x height
In this case, the density of oil is given as 0.775 g/mL, which is equivalent to 0.775 g/cm³. The height of the oil column is given as 7.68 cm. And g represents the acceleration due to gravity, which is approximately 9.8 m/s².
Converting the given values to proper units, we have:
Density = 0.775 g/cm³
Height = 7.68 cm
g = 9.8 m/s²
Density = 0.775 g/cm³ x 1 g/mL
Density = 0.775 g/mL
Density = 0.775 g/mL x (1 mL/1 cm³)
Density = 0.775 g/cm³
Plugging in the values, we have:
Poil = 0.775 g/cm³ x 9.8 m/s² x 7.68 cm
Poil = 56.2064 g/(cm² x s²)
Now, let's calculate Pg using the equation for pressure difference in the manometer (assuming the oil is in the left limb):
Pg - Pbar = Poil
We want to find Pg, so rearranging the equation:
Pg = Pbar + Poil
Substituting the known values, we have:
Pg = 760.0 mmHg + 56.2064 g/(cm² x s²)
Calculating this sum:
Pg = 816.2064 mmHg
Therefore, the pressure of the gas in the flask is 816.2064 mmHg.