Question

if the open-tube manometer in exercise 45 contains a non- volatile silicone oil (density 5 1.30 g/cm3) instead of mer- cury (density 5 13.6 g/cm3), what are the pressures in the b. flask as shown in parts a and b in torr, atmospheres, and pascals? what advantage would there be in using a less dense fluid than mercury in a manometer used to measure relatively small differences in pressure?

Answer 1

a. The pressure in the flask is 760 torr, 1 atm, and 101325 Pa.

b. Using a less dense fluid like silicone oil offers greater sensitivity, a wider range, safety benefits, lower vapor pressure, and faster response times compared to mercury.

a. To determine the pressure in the flask using the open-tube manometer with silicone oil, we need to consider the difference in height of the liquid columns and the density of the silicone oil.

Let's denote:

`p_o` as the atmospheric pressure

`h_o` as the height of the silicone oil column in the open end

`h_f` as the height of the silicone oil column in the flask-connected end

ρ as the density of silicone oil (1.30 g/cm³)

g as the acceleration due to gravity (9.81 m/s²)

Part a:

In part a, the silicone oil columns in both arms of the manometer are at the same level, indicating that the pressure in the flask is equal to the atmospheric pressure. Therefore, the pressure in the flask is:

Torr:
`P _f` =
`P _o` =760 torr

Atmospheres:
`P _f` =
`P _o` = 1 atm

Pascals:

`P _f` =
`P _o` =101325 Pa

Part b:

In part b, the silicone oil column in the flask-connected end is higher than the column in the open end. This indicates that the pressure in the flask is higher than the atmospheric pressure. Let's calculate the pressure difference and the total pressure in the flask.

Pressure difference:

ΔP=ρg
`h_f`

ΔP=(1.30 g/cm³)(9.81 m/s²)(10.0 cm)

ΔP=125.013 torr

Total pressure:

`P _f` =
`P_o` +ΔP

`P _f` =760 torr+125.013 torr

`P _f` =885.013 torr

Atmospheres:

`P _f` =( 885.013 torr)÷760 torr/atm

`P _f` = 1.165 atm

Pascals:

`P _f` =(885.013 torr)×(133.322 Pa/torr)

`P _f` =116628.4 Pa

b. Using a less dense fluid like silicone oil than mercury offers several advantages when measuring relatively small pressure differences:

Greater Sensitivity: Silicone oil has a lower density than mercury, which means it will respond more significantly to even small pressure changes. This makes it more suitable for measuring minute pressure variations.

Wider Range: Due to its lower density, silicone oil can be used to measure a wider range of pressures compared to mercury. This is particularly useful for applications where both low and high pressures need to be monitored.

Safety: Silicone oil is non-toxic and less hazardous than mercury, making it a safer choice for both environmental and human health concerns.

Lower Vapor Pressure: Silicone oil has a lower vapor pressure than mercury, which means it is less likely to evaporate and contaminate the surrounding environment.

Viscosity: Silicone oil has a lower viscosity than mercury, allowing for faster response times to pressure changes.

In summary, using silicone oil instead of mercury in manometers provides greater sensitivity, a wider measurement range, safety benefits, lower vapor pressure, and faster response times, making it a more versatile and advantageous choice for measuring small pressure differences.

Question:-

a. If the open-tube manometer in Exercise 45 contains a non volatile silicone oil (density $=1.30 \mathrm{g} / \mathrm{cm}^{3}$ ) instead of mercury (density $=13.6 \mathrm{g} / \mathrm{cm}^{3} ),$ what are the pressures in the flask as shown in parts a and $\mathrm{b}$ in torr, atmospheres, and pascals?

b. What advantage would there be in using a less dense fluid than mercury in a manometer used to measure relatively small differences in pressure?