Unit 14: Gases

The Sun is the primary source of energy, and Earth’s gravity is what prevents the atmosphere from flying off into space.

Solar energy, radiated in the form of electromagnetic waves, is the primary source of energy for Earth’s climate system.

Earth’s gravitational force is strong enough to pull on the atmosphere and keep it around our planet. Any particle (including an air molecule) moving up toward outer space experiences downward acceleration due to gravity, which can bring it down closer to the surface. Some molecules, however, do acquire speeds greater than 11.2 km/s (the escape velocity) and may leave the atmosphere forever.

Note that the escape velocity on the Moon (2.4 km/s) is relatively small, which explains the absence of a lunar atmosphere.

1. 1 N.
2. The balloon descends.
3. The balloon ascends.

When suspended in air, the balloon experiences a net force equal to zero. Therefore, the 1-N weight of the balloon is balanced by an equal (buoyant) force in the upward direction. If the buoyant force decreases, the balance is broken, which causes the downward gravitational force (or weight) to overcome the smaller upward buoyant force. As a result, the balloon drifts down. The opposite happens when the buoyant force increases.

8.3 km above Earth’s surface.

The mass of an air column above 1 m² of Earth’s surface is calculated as follows: \begin{align} \text{Mass of air column} &= \frac{\text{weight}}{g} \nonumber\\[6pt] &= \frac{100{,}000\,\text{N}}{10\,\text{m}/\text{s}^2} \nonumber\\[6pt] &= 10{,}000\,\text{kg} \end{align} You can calculate the volume of this amount of air by using the following formula: \begin{align} \text{Volume of air column} &= \frac{\text{mass}}{\text{density}} \nonumber\\[6pt] &= \frac{10{,}000\,\text{kg}}{1.2\,\text{kg}/\text{m}^3} \nonumber\\[6pt] &= 8300\,\text{m}^3 \end{align} Now you can find the height of the column, which is where the top of the atmosphere would be: \begin{align} \text{Height of air column} &= \frac{\text{volume}}{\text{area}} \nonumber\\[6pt] &= \frac{8300\,\text{m}^3}{1\,\text{m}^2} \nonumber\\[6pt] &= 8300\,\text{m} \quad (\text{or}\; 8.3\,\text{km}) \end{align} This is approximately equal to the elevation of Mt. Everest!

The air inside the ball expands to restore the pressure balance.

The air pressure inside the underinflated football at sea level is equal to the surrounding atmospheric pressure. When you take it to the top of a mountain, the ball experiences less inward force on the external walls due to the reduced atmospheric pressure. As a result, the compressed air inside pushes outward on the internal walls, causing the ball to expand until the internal pressure reduces to the atmospheric pressure outside the ball.

To withstand the large difference in pressure between the outside and inside air.

Commercial airplanes normally fly at altitudes of approximately 10 km, where the outside atmospheric pressure is nearly one-quarter its value at sea level. The comfortable pressure maintained inside the airplane is close to the normal atmospheric pressure near ground level. Such a considerable pressure difference results in an outward force on the plane’s windows proportional to their area. So doubling the size of a window would double the outward force and make it unsafe during flight.

152 cm

The height of the column of mercury in a standard barometer is 76 cm at normal atmospheric pressure. If a liquid of half the density of mercury were used instead, you would need to double the column length for it to have the same weight as the mercury column.

No.

The buoyant force on an object depends on its volume, not its mass. Therefore, two balloons of the same size experience equal buoyant forces regardless of the gas inside. The net lift, however, is greater for the hydrogen balloon because it has a smaller weight than the helium balloon.

Consider the weight of an empty steel tank compared with the buoyant force.

The weight of the steel tank is greater than the buoyant force.

The walls of a steel tank are much heavier than a regular rubber balloon. So even when the tank is filled with helium, its total weight is greater than the weight of displaced air. Consequently, the net force on the tank (weight minus buoyant force) is directed downward and keeps the tank on the ground.

A helium-filled balloon experiences an upward buoyant force greater than its weight because the air displaced by the balloon is heavier than the combined weight of the rubber and enclosed helium gas.

1. Its speed increases.
2. Its pressure decreases.
3. Its streamlines get closer to each other.

The speed of the gas increases when it enters the section of the pipe with a smaller cross-sectional area. This is because the same flow rate is maintained throughout the pipe, meaning that equal quantities of the gas pass through each section of the pipe during a specific time interval. As the gas passes through the narrow section, it flows faster and its pressure decreases, according to Bernoulli’s principle. The spacing between streamlines decreases, as the streamlines must squeeze together to fit into the slimmer pipe.

They will move closer to each other.

As you blow between the sheets, the pressure in the fast-moving air becomes less than the atmospheric pressure on the outer sides of the sheets, according to Bernoulli’s principle. As a result, the sheets are pushed closer to each other.

When a moving gas molecule bounces off the wall of a container, a force is exerted on the wall during impact. The gas pressure is proportional to the number of such impacts on the container walls per unit time. As a result, doubling the number of gas molecules inside the container (while maintaining the same temperature) causes the pressure to increase to twice the initial value.

Note that higher temperature means faster-moving molecules and harder impacts on the container walls, resulting in increased pressure.