Conceptual Physics

Step-by-step solution

Patm is known. We find PH2O and add the two quantities together to find the absolute pressure Pabs.

Step Reason

1. Patm = 1.013×10^5 Pa standard value

2. PH2O = ȡgh gauge pressure equation

3. substitute values

4. PH2O = 4.90×10^5 Pa evaluate

5. Pabs = PH2O + Patm absolute pressure

6. substitute equations 1 and 4 into equation 5

13.6 - Physics at work: measuring pressure

Atmospheric pressure is not constant, even at a fixed

height like sea level. In Concept 1, you see a simple

barometer. Barometers measure atmospheric

pressure. The terms “barometer” and “barometric

pressure” are sometimes heard in weather reports

because changes in atmospheric pressure often

indicate that a change of weather is on the way.

The barometer depicted on the right consists of a

vertical tube, closed at the top. This tube is partially

filled with a liquid, commonly the liquid metal mercury,

and is placed in a container that serves as a

reservoir. The mercury in the tube stands in a column,

with the space at the top of the tube occupied by a

near vacuum, which exerts negligible pressure.

Increased air pressure pushing down on the surface of the reservoir causes the column

of mercury to rise, until the air pressure and the pressure due to the mercury column

reach equilibrium. The pressure exerted by this liquid column, the product of its density,

the acceleration of gravity, and its height, equals the external air pressure.

On a typical day at sea level, air pressure causes the mercury to rise to a height of

about 760 millimeters, or about 30 inches. (The pressure of a one-millimeter column of

mercury is called a torr, after the physicist Evangelista Torricelli.) The design of this

instrument should give you a sense of how strong atmospheric pressure is: It is able to

force a column of mercury, which is denser than lead, to rise more than three-quarters

of a meter.

In Concept 2 you see an open-tube manometer, a device for measuring the gauge

pressure of a gas confined in a spherical vessel. The vessel that contains the gas is

connected to a U-shaped tube partially filled with mercury and open to the atmosphere

at its far end. This apparatus allows physicists to accurately determine the gauge

pressure of the gas.

The pressure inside the spherical vessel on the left-hand side is an absolute pressure. It

presses down on the surface of the left-hand column of mercury, but the higher column

of mercury and the air pressure on the right side push back. When the two columns of

mercury are in equilibrium, the absolute pressure of the gas equals the sum of the

atmospheric pressure and the pressure exerted by the extra mercury on the right-hand

side of the instrument. This equality is shown in Equation 2. In the equation, the product

ȡgh represents the pressure exerted by a column of mercury of height h.

The height h of the extra mercury, indicated in the diagram, equals the amount by which

the mercury level on the right is higher than the mercury level on the left. It can be used

with the density of mercury and the acceleration of gravity to calculate the product ȡgh.

This product equals the difference between the absolute pressure of the gas in the

vessel and atmospheric pressure. In other words, the product ȡgh gives the gauge

pressure of the gas, in pascals. When the gauge pressure is expressed in “millimeters

of mercury,” or torr, then its numeric value equals the numeric value of the height h,

measured in millimeters.

Dial-type barometer, calibrated in millimeters of mercury and millibars.

Barometer

Air pressure equals pressure of mercury

·Height of mercury reflects air pressure

Open-tube manometer

Vessel pressure

= atm pressure + mercury pressure

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