Fluids: Liquids and Gases

Pressure in Gases

A Familiar Gas

We live at the bottom of a 100 km thick blanket of gases - we call it the atmosphere. It is not very dense, and we don’t have to propel our way though it, as we do when swimming in water. The atmosphere has mass and pushes down on us. The pressure of the atmosphere is 10 N/cm2 or 105 N/m2. The force of the atmosphere is substantial. For example, if your hold your palm up (with an area of about 150 cm2) the force on it is, remembering that P = F/A,

F = PA = 10 N/cm2 * 150 cm2 = 1500 N

This is about 330 pounds! But remember the air surrounds you so that there is also 1500 N pushing up on the bottom of your hand – that is why you aren’t smacked down by air.

Other planets in our solar system have atmospheres that are composed of different molecules and have different densities. The atmospheres of both Mars and Venus are almost entirely CO2, but Mars has only a tiny amount so its atmospheric pressure is only about 6% as much as Earth’s. Venus has a thick and heavy atmosphere with a pressure 92 times as much as on Earth. In addition to the heavy atmosphere, the surface temperature on Venus is 460 °C. Only a few space probes have landed on Venus and they have lasted only an hour or two before being squashed and melted.

One other peculiar atmosphere is that of Saturn’s large moon Titan. Its atmosphere is nitrogen and methane, and it has ten times the atmospheric pressure as Earth and its temperature is -179°C.

Earth’s atmospheric pressure varies with elevation – climbers of Mt Everest usually carry oxygen bottles because air pressure at the summit is only one third as much as at sea level - there just isn’t enough air for comfortable breathing. Pressure also changes according to the weather, and atmospheric pressure changes are measured with a barometer. Barometers were traditionally made as tall tubes of mercury that were turned upside down into a container of mercury, resulting in a vacuum at the top of the tube. The air pressure on the surface of the mercury in the container supported a column of mercury about 76 cm high. The ruler near the top of the tube provided a scale for making accurate measurements of the height of the mercury.  Mercury is used because it is 13.6 times more dense than water; water barometers would be about 10 m tall - about the same height as a basketball team standing on each other's shoulders.

It is inconvenient to carry cylinders of mercury when climbing mountains so barometers were invented that use a small box made of flexible metal. As air pressure increases, the box is squeezed smaller; when it decreases, a spring inside causes it to expand. Mechanical levers translate the small volume changes to a pointer that rotates around a dial. Such aneroid barometers can be made small enough to fit within a smart phone.

Why would you want to take a barometer with you when climbing a mountain? Because pressure decreases with  altitude, so the barometer, when corrected for temperature, gives your elevation. Before aneroid barometers were used explorers in Africa in the mid-1800s used to “boil the thermometer” to see what the temperature was when water boiled. Because air pressure decreases with elevation, water requires less heat, and thus lower temperature, to boil. At sea level water boils at 100°C, but at 3,000 m elevation it boils at 90°C. After the explorers measured the temperature of the boiling water they could use it to make tea.