If a Gas Pressure Gauge Reads 31.6 in. Hg What Is the Pressure in Millimeters of Mercury

Chapter 9 Lecture Notes

Learning Objectives

By the end of this section, you volition be able to:

• Define the property of pressure
• Ascertain and convert among the units of pressure measurements
• Depict the operation of common tools for measuring gas pressure
• Calculate pressure from manometer information

The earth's atmosphere exerts a pressure, every bit does whatsoever other gas. Although nosotros do not normally discover atmospheric pressure, we are sensitive to pressure changes—for instance, when your ears "pop" during take-off and landing while flight, or when you swoop underwater. Gas pressure is caused by the strength exerted by gas molecules colliding with the surfaces of objects (Figure 1). Although the force of each collision is very small, whatever surface of appreciable surface area experiences a big number of collisions in a short time, which can upshot in a high force per unit area. In fact, normal air pressure is potent enough to crush a metal container when non balanced past equal pressure from inside the container.

Effigy 1. The atmosphere above usa exerts a big force per unit area on objects at the surface of the earth, roughly equal to the weight of a bowling ball pressing on an area the size of a human thumbnail.

A dramatic illustration of atmospheric force per unit area is provided in this brief video, which shows a railway tanker car imploding when its internal force per unit area is decreased.

A smaller calibration demonstration of this miracle is briefly explained in the post-obit video:

Atmospheric pressure level is caused past the weight of the cavalcade of air molecules in the atmosphere higher up an object, such as the tanker car. At sea level, this pressure is roughly the same as that exerted by a total-grown African elephant standing on a doormat, or a typical bowling ball resting on your thumbnail. These may seem like huge amounts, and they are, but life on world has evolved nether such atmospheric pressure. If yous really perch a bowling ball on your thumbnail, the pressure experienced is twice the usual pressure, and the sensation is unpleasant.

In general, pressure is divers as the force exerted on a given expanse: [latex]P=\frac{F}{A}.[/latex] Annotation that pressure is directly proportional to force and inversely proportional to area. Thus, pressure tin be increased either past increasing the amount of force or past decreasing the area over which information technology is applied; pressure can be decreased by decreasing the force or increasing the area.

Permit's apply this concept to determine which would be more than likely to autumn through thin ice in Figure 2—the elephant or the effigy skater? A large African elephant can weigh seven tons, supported on 4 anxiety, each with a bore of about 1.5 ft (footprint area of 250 in²), and so the force per unit area exerted by each human foot is well-nigh xiv lb/in²:

[latex]\text{pressure per elephant foot}=\text{14,000}\frac{\text{lb}}{\text{elephant}}\times \frac{\text{1 elephant}}{\text{4 anxiety}}\times \frac{\text{1 foot}}{250{\text{in}}^{2}}=14{\text{lb/in}}^{2}[/latex]

The figure skater weighs near 120 lbs, supported on two skate blades, each with an surface area of well-nigh 2 inⁱⁱ, so the pressure exerted by each blade is about xxx lb/in^two:

[latex]\text{pressure per skate bract}=120\frac{\text{lb}}{\text{skater}}\times \frac{\text{1 skater}}{\text{2 blades}}\times \frac{\text{1 blade}}{2{\text{in}}^{2}}=thirty{\text{lb/in}}^{2}[/latex]

Even though the elephant is more than than ane hundred-times heavier than the skater, it exerts less than half of the pressure and would therefore exist less likely to fall though thin ice. On the other mitt, if the skater removes her skates and stands with bare feet (or regular footwear) on the water ice, the larger area over which her weight is applied profoundly reduces the pressure level exerted:

[latex]\text{pressure per human foot}=120\frac{\text{lb}}{\text{skater}}\times \frac{\text{1 skater}}{\text{2 feet}}\times \frac{\text{i pes}}{30{\text{in}}^{2}}=2{\text{lb/in}}^{2}[/latex]

Effigy two. Although (a) an elephant'due south weight is large, creating a very large forcefulness on the ground, (b) the figure skater exerts a much higher pressure on the ice due to the pocket-size surface area of her skates. (credit a: modification of work by Guido da Rozze; credit b: modification of work by Ryosuke Yagi)

The SI unit of measurement of pressure is the pascal (Pa), with 1 Pa = 1 N/m², where North is the newton, a unit of strength defined as 1 kg 1000/s². Ane pascal is a small pressure; in many cases, information technology is more than convenient to use units of kilopascal (1 kPa = 1000 Pa) or bar (i bar = 100,000 Pa). In the United States, pressure level is often measured in pounds of forcefulness on an area of one square inch—pounds per square inch (psi)—for instance, in automobile tires. Pressure tin can also exist measured using the unit atmosphere (atm), which originally represented the boilerplate sea level air pressure at the gauge latitude of Paris (45°). Table one provides some data on these and a few other common units for pressure measurements

Tabular array i. Pressure Units
Unit Name and Abbreviation	Definition or Relation to Other Unit of measurement
pascal (Pa)	1 Pa = 1 N/m2 recommended IUPAC unit
kilopascal (kPa)	1 kPa = grand Pa
pounds per square inch (psi)	air pressure level at sea level is ~xiv.7 psi
temper (atm)	1 atm = 101,325 Pa air pressure at sea level is ~1 atm
bar (bar, or b)	1 bar = 100,000 Pa (exactly) commonly used in meteorology
millibar (mbar, or mb)	chiliad mbar = 1 bar
inches of mercury (in. Hg)	i in. Hg = 3386 Pa used by aviation industry, also some weather reports
torr	[latex]\text{1 torr}=\frac{\text{1}}{\text{760}}\text{atm}[/latex] named after Evangelista Torricelli, inventor of the barometer
millimeters of mercury (mm Hg)	i mm Hg ~1 torr

Instance 1: Conversion of Pressure level Units

The Usa National Weather Service reports pressure level in both inches of Hg and millibars. Convert a pressure level of 29.2 in. Hg into:

1. torr
2. atm
3. kPa
4. mbar

Check Your Learning

A typical barometric pressure in Kansas Metropolis is 740 torr. What is this pressure in atmospheres, in millimeters of mercury, in kilopascals, and in bar?

Testify Answer

0.974 atm; 740 mm Hg; 98.7 kPa; 0.987 bar

We tin measure atmospheric pressure, the forcefulness exerted by the atmosphere on the globe's surface, with a barometer (Effigy iii). A barometer is a drinking glass tube that is airtight at one end, filled with a nonvolatile liquid such as mercury, and then inverted and immersed in a container of that liquid. The atmosphere exerts pressure on the liquid outside the tube, the column of liquid exerts force per unit area inside the tube, and the pressure at the liquid surface is the same within and exterior the tube. The tiptop of the liquid in the tube is therefore proportional to the pressure exerted by the atmosphere.

Figure 3. In a barometer, the height, h, of the cavalcade of liquid is used every bit a measurement of the air pressure. Using very dense liquid mercury (left) permits the construction of reasonably sized barometers, whereas using water (right) would require a barometer more than xxx feet tall.

If the liquid is h2o, normal atmospheric pressure will support a column of water over 10 meters loftier, which is rather inconvenient for making (and reading) a barometer. Because mercury (Hg) is well-nigh thirteen.6-times denser than water, a mercury barometer only needs to be [latex]\frac{1}{13.vi}[/latex] as alpine every bit a water barometer—a more suitable size. Standard atmospheric pressure level of one atm at sea level (101,325 Pa) corresponds to a column of mercury that is almost 760 mm (29.92 in.) high. The torr was originally intended to be a unit equal to one millimeter of mercury, only it no longer corresponds exactly. The pressure exerted by a fluid due to gravity is known as hydrostatic pressure, p:

[latex]p=h\rho g[/latex]

where h is the height of the fluid, ρ is the density of the fluid, and g is acceleration due to gravity.

Case 2: Adding of Barometric Pressure

Prove the calculation supporting the claim that atmospheric pressure about sea level corresponds to the force per unit area exerted by a column of mercury that is near 760 mm loftier. The density of mercury = xiii.6 g/cm^three.

Bank check Your Learning

Calculate the height of a column of water at 25 °C that corresponds to normal atmospheric pressure. The density of water at this temperature is 1.0 g/cm³.

A manometer is a device similar to a barometer that tin can be used to measure the pressure of a gas trapped in a container. A closed-end manometer is a U-shaped tube with ane airtight arm, one arm that connects to the gas to be measured, and a nonvolatile liquid (usually mercury) in between. Every bit with a barometer, the distance between the liquid levels in the two arms of the tube (h in the diagram) is proportional to the pressure of the gas in the container. An open up-terminate manometer (Figure 4) is the aforementioned as a closed-finish manometer, simply one of its arms is open up to the atmosphere. In this case, the distance between the liquid levels corresponds to the departure in pressure between the gas in the container and the temper.

Figure iv. A manometer can be used to measure the pressure of a gas. The (deviation in) height between the liquid levels (h) is a mensurate of the force per unit area. Mercury is usually used because of its big density.

Case 3: Calculation of Pressure Using a Closed-Cease Manometer

The pressure of a sample of gas is measured with a closed-cease manometer, every bit shown below.

The liquid in the manometer is mercury. Decide the pressure level of the gas in:

1. torr
2. Pa
3. bar

Check Your Learning

The pressure of a sample of gas is measured with a closed-end manometer. The liquid in the manometer is mercury.

Determine the pressure of the gas in:

1. torr
2. Pa
3. bar

Example 4: Calculation of Pressure Using an Open-End Manometer

The force per unit area of a sample of gas is measured at sea level with an open-end Hg (mercury) manometer, every bit shown below.

Determine the pressure of the gas in:

1. mm Hg
2. atm
3. kPa

Cheque Your Learning

The pressure of a sample of gas is measured at sea level with an open up-end Hg manometer, as shown below.

Make up one's mind the force per unit area of the gas in:

1. mm Hg
2. atm
3. kPa

Exercises

1. The pressure of a sample of gas is measured at bounding main level with a closed-end manometer. The liquid in the manometer is mercury.
   
   Decide the pressure of the gas in:
   1. torr
   2. Pa
   3. bar
2. The pressure of a sample of gas is measured with an open-end manometer, partially shown to the correct. The liquid in the manometer is mercury.
   
   Assuming atmospheric pressure is 29.92 in. Hg, determine the pressure of the gas in:
   1. torr
   2. Pa
   3. bar
3. The force per unit area of a sample of gas is measured at sea level with an open-end mercury manometer.
   
   Assuming atmospheric pressure is 760.0 mm Hg, determine the force per unit area of the gas in:
   1. mm Hg
   2. atm
   3. kPa
4. The force per unit area of a sample of gas is measured at ocean level with an open up-stop mercury manometer.
   
   Assuming atmospheric force per unit area is 760 mm Hg, determine the force per unit area of the gas in:
   1. mm Hg
   2. atm
   3. kPa

Measuring Blood Pressure

Blood pressure level is measured using a device called a sphygmomanometer (Greek sphygmos = "pulse"). It consists of an inflatable cuff to restrict blood flow, a manometer to mensurate the pressure level, and a method of determining when claret flow begins and when it becomes impeded (Figure five). Since its invention in 1881, information technology has been an essential medical device. At that place are many types of sphygmomanometers: transmission ones that require a stethoscope and are used by medical professionals; mercury ones, used when the most accuracy is required; less accurate mechanical ones; and digital ones that tin can exist used with little training but that have limitations. When using a sphygmomanometer, the gage is placed effectually the upper arm and inflated until blood period is completely blocked, then slowly released. Every bit the middle beats, claret forced through the arteries causes a rising in pressure level. This rise in pressure level at which blood period begins is the systolic pressure—the tiptop force per unit area in the cardiac wheel. When the cuff's pressure equals the arterial systolic force per unit area, blood flows past the cuff, creating audible sounds that can be heard using a stethoscope. This is followed by a subtract in pressure level as the heart's ventricles ready for another beat. As cuff pressure level continues to decrease, eventually sound is no longer heard; this is the diastolic pressure—the everyman pressure level (resting stage) in the cardiac bike. Blood pressure level units from a sphygmomanometer are in terms of millimeters of mercury (mm Hg).

Figure 5. (a) A medical technician prepares to measure a patient's blood pressure with a sphygmomanometer. (b) A typical sphygmomanometer uses a valved safety bulb to inflate the cuff and a diaphragm estimate to measure pressure. (credit a: modification of work by Master Sgt. Jeffrey Allen)

Meteorology, Climatology, and Atmospheric Science

Throughout the ages, people take observed clouds, winds, and precipitation, trying to discern patterns and make predictions: when information technology is best to plant and harvest; whether it is rubber to set out on a sea voyage; and much more. Nosotros now confront circuitous atmospheric condition and atmosphere-related challenges that will accept a major touch on our civilization and the ecosystem. Several different scientific disciplines use chemical principles to help us better empathize weather, the temper, and climate. These are meteorology, climatology, and atmospheric science. Meteorology is the report of the atmosphere, atmospheric phenomena, and atmospheric effects on earth's weather. Meteorologists seek to sympathize and predict the weather in the short term, which can salve lives and benefit the economy. Weather forecasts (Effigy 6) are the result of thousands of measurements of air pressure, temperature, and the like, which are compiled, modeled, and analyzed in weather centers worldwide.

Figure half dozen. Meteorologists employ weather maps to describe and predict weather. Regions of high (H) and low (L) pressure take large furnishings on atmospheric condition conditions. The gray lines represent locations of constant force per unit area known equally isobars. (credit: modification of work by National Oceanic and Atmospheric Administration)

In terms of atmospheric condition, low-pressure systems occur when the globe'south surface atmospheric pressure is lower than the surrounding environment: Moist air rises and condenses, producing clouds. Movement of moisture and air within various conditions fronts instigates near atmospheric condition events.

The atmosphere is the gaseous layer that surrounds a planet. Globe's atmosphere, which is roughly 100–125 km thick, consists of roughly 78.one% nitrogen and 21.0% oxygen, and tin can be subdivided farther into the regions shown in Effigy 7: the exosphere (furthest from globe, > 700 km above sea level), the thermosphere (80–700 km), the mesosphere (l–80 km), the stratosphere (second everyman level of our atmosphere, 12–50 km above sea level), and the troposphere (up to 12 km to a higher place sea level, roughly 80% of the earth's atmosphere by mass and the layer where nearly weather events originate). As you go higher in the troposphere, air density and temperature both subtract.

Effigy 7. Earth's atmosphere has five layers: the troposphere, the stratosphere, the mesosphere, the thermosphere, and the exosphere.

Climatology is the study of the climate, averaged weather conditions over long time periods, using atmospheric data. However, climatologists study patterns and effects that occur over decades, centuries, and millennia, rather than shorter time frames of hours, days, and weeks like meteorologists. Atmospheric science is an fifty-fifty broader field, combining meteorology, climatology, and other scientific disciplines that study the atmosphere.

Cardinal Concepts and Summary

Gases exert pressure, which is pressure level. The pressure of a gas may exist expressed in the SI unit of pascal or kilopascal, as well as in many other units including torr, atmosphere, and bar. Atmospheric pressure is measured using a barometer; other gas pressures tin can exist measured using one of several types of manometers.

Key Equations

• [latex]P=\frac{F}{A}[/latex]
• p = hρg

Exercises

1. Why are sharp knives more effective than dull knives (Hint: think about the definition of pressure)?
2. Why do some small bridges have weight limits that depend on how many wheels or axles the crossing vehicle has?
3. Why should you roll or belly-crawl rather than walk across a thinly-frozen pond?
4. A typical barometric pressure level in Redding, California, is about 750 mm Hg. Calculate this force per unit area in atm and kPa.
5. A typical barometric pressure in Denver, Colorado, is 615 mm Hg. What is this pressure in atmospheres and kilopascals?
6. A typical barometric force per unit area in Kansas City is 740 torr. What is this pressure in atmospheres, in millimeters of mercury, and in kilopascals?
7. Canadian tire pressure gauges are marked in units of kilopascals. What reading on such a judge corresponds to 32 psi?
8. During the Viking landings on Mars, the atmospheric pressure was determined to be on the average about 6.50 millibars (1 bar = 0.987 atm). What is that force per unit area in torr and kPa?
9. The pressure of the atmosphere on the surface of the planet Venus is nigh 88.8 atm. Compare that pressure in psi to the normal pressure on world at sea level in psi.
10. A medical laboratory catalog describes the pressure level in a cylinder of a gas equally 14.82 MPa. What is the pressure level of this gas in atmospheres and torr?
11. Consider this scenario and answer the post-obit questions: On a mid-August day in the northeastern United States, the following data appeared in the local newspaper: atmospheric pressure level at sea level 29.97 in., 1013.9 mbar.
    1. What was the pressure in kPa?
    2. The pressure level almost the seacoast in the northeastern U.s. is usually reported about xxx.0 in. Hg. During a hurricane, the pressure may fall to near 28.0 in. Hg. Calculate the drop in pressure level in torr.
12. Why is it necessary to employ a nonvolatile liquid in a barometer or manometer?
13. How would the utilize of a volatile liquid affect the measurement of a gas using open-ended manometers vs. closed-end manometers?

Glossary

temper (atm):unit of pressure; i atm = 101,325 Pa

bar:(bar or b) unit of pressure; 1 bar = 100,000 Pa

barometer:device used to measure out atmospheric pressure

hydrostatic pressure level:pressure exerted by a fluid due to gravity

manometer:device used to measure the pressure level of a gas trapped in a container

pascal (Pa):SI unit of pressure; 1 Pa = 1 N/grand²

pounds per square inch (psi):unit of pressure level common in the United states of america

pressure:force exerted per unit area

torr:unit of pressure; [latex]\text{one torr}=\frac{one}{760}\text{atm}[/latex]

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