Gas Laws and Global Effects - Gasgeset­ze und Globale Auswirku­ngen

P₁=1atm

V₁=5000cm3

P₂=4atm

V₂=?

At 4atm the diver’s lungs is crushed to 1250cm3. The further down the diver descends the more the lungs are crushed (decrease in volume). Luckily scuba gear prevents Boyles’ law from happening. Scuba tanks are capable of equalizing the air being breathed in so that its pressure is equal to the external pressure (pressure exerted by water on diver) (Gibb, 2011).

No change in pressure means no change in volume. As a result the lungs are not crushed.

Boyle’s law also applies as the diver ascends. As a diver ascends the pressure decreases and the volume of air in his/her lungs increases. If the diver ascends too quickly, without equalizing the air pressure in his lungs regularly, the expansion of volume of air would be too rapid and will stretch or even explode the lungs, whose volume does not change (Gibb, 2011).

To illustrate consider the following case: That same diver at 30m (4atm) suddenly ascends to sea level. The average lung capacity is 5000cm3as stated before.

P₁=4atm

V₁=5000cm3

P₂=1atm

V₂=?

The volume of air would expand to 20 000cm3 when a divers lungs can only hold 5000cm3. The trapped air must escape and consequently explodes the lungs. That is why “never hold your breath” while scuba diving.

In much the same way Boyles’ law combined with Henry’s law also explains a diver’s sickness called Bends. Bends causes severe pain which is due to the forming of nitrogen bubbles in joints. This happens when nitrogen, which is not used up (unlike oxygen), from the bloodstream is released as the diver ascends to the surface rapidly (Lliff, 2008). To understand why, Henry law must be understood.

Henry’s law states that as the pressure increases, the solubility of a gas increases (wilbraham, staley, & matta, 1995). This is illustrated in the below graph.

Similarly the deeper the diver dives (more pressure) the more nitrogen is absorbed into the bloodstream. This can also be illustrate using henry’s law which can be expressed as;

 (Peter J. Mikulecky, Brutlag, Gilman, & Peterson, 2008).

At 1atm (25ᴼC) the solubility of N₂ is 4.88x104mol/L. What is the solubility at 5atm (40m)?

P₁=1atm

S₂=?

P₂=5atm

As the diver ascends (less pressure) the solubility of blood decreases and the absorbed nitrogen must escape. It escapes by forming nitrogen bubbles which gather at the joints. The faster the diver ascends the more bubbles formed and the more painful and severe the effects of bends become (Lliff, 2008). Other factors that affect solubility of nitrogen are time and temperature.

Below is a graph showing the relationship between temperature and solubility of nitrogen.

With temperature declines the solubility of nitrogen increases. The means more nitrogen can be dissolved in the bloodstream in cooler water. This also true for more time, more time more nitrogen dissolved (Lliff, 2008). For this reason and the reason stated above it is important to ascend slowly.

Dalton’s law of partial pressure state that, at constant temperature, the total pressure of a gas mixture is equal to the sum of its partial pressures (wilbraham, staley, & matta, 1995). Partial pressure is the pressure exerted by each component of a gas mixture (wilbraham, staley, & matta, 1995). As pressure increases partial pressure of each gas in the mixture increases also.

At sea level (1atm) partial pressure of O₂=0.21atm.

At 8atm (70m) what will be the partial pressure of oxygen?

Whileoxygen is essential for survival, if the partial pressure of oxygen being breathed in exceed 1.6atm (the maximum partial pressure of oxygen humans nervous system can sustain) it becomes toxic (Pohl, 2008). Understanding Dalton’s law give divers better understanding of the limits set by diving tables.

Lastly Boyle’s law effect buoyancy. Buoyancy describes an objects tendency to float (ConjectureCorporation, 2008). To work out a divers’ buoyancy and whether they will float, sink or neither, Archimedes’ principle can be used. Archimedes’ realised that an object immersed in fluid is buoyed up by a force equal to the weight of the fluid the object displaces. This is called the buoyant force (ConjectureCorporation, 2008).      

1.       Gravity and weight of the object/diver+all equipment

2.       buoyancy or buoyant force

If the gravity and the weight of the object is heavier than the weight of the water it has displaced (buoyant force) then it will have negative buoyancy (diver sinks). If the situation is reversed the diver will have positive buoyancy (diver floats). If both forces are equal diver will have neutral buoyancy and will remain at same level (Gibb, 2011).

How is Boyle’s law related to buoyancy?

Boyle’s law affects scuba equipment; mainly the Buoyancy Control Device (BCD) and scuba suit. As pressure increases the volume the BCD and scuba suit occupies decreases; its mass is still the same. This in turn results in a decrease of the buoyant force as the weight of the water being displaced is less. As the mass is still the same but less buoyancy the diver sinks.

Finally there is Gay-Lussac’s law which states at constant volume, increases in temperature and pressure is directly proportional. Gay-Lussac’s law explains why a scuba tank can burst in the hot boot of a car. Since the volume of a scuba tank is fixed as its temperature increases so does the pressure (wilbraham, staley, & matta, 1995).

Another real life scenario that concern gas laws is hot air balloons. A hot air balloon is made up of 3 main parts (Eballoon.org, N.D.):

·         The Envelope 
The actual fabric balloon which holds the air

·         The Burner
The unit which propels the heat up inside the envelope and inflates it.

·         The Basket
Where the passengers and pilot stand

Using the rearranged formula the density of air at different temperatures can be calculated.

At 25ᴼC what is the density of dry air? Given the molar mass of air is 28.97mol/L (EngineeringToolbox, 2007).

M_{dry air}=28.97mol/L

P=1atm

R=0.08026(Lxatm)/(kxmol)

T=298K

At 100ᴼC the density of dry air is?

M_{dry air}=28.97mol/L

P=1atm

R=0.08026(Lxatm)/(kxmol)

T=373K

As clearly shown the density of air is less as temperature escalates. But in order for the hot air balloon to float or rise up in the fluid (air) the buoyant force (the air displaced by the hot air balloon) must be greater than the mass of the entire balloon (downward force -passengers, basket, etc.). This is according to Archimedes principle, as stated previously (ConjectureCorporation, 2008).

m=lift of balloon, how much mass the balloon is able to lift in kilograms.

Ambient density of dry air-density of air surrounding the hot air balloon.

= internal density of dry air -density of dry air inside envelope of hot air balloon ()

V=volume of the balloon in m3.

The following is an example of how Archimedes formula can be applied. For this example the previously calculated external and internal densities of dry air will be used. The volume of a four person hot air balloon is 2200m3 (FlyMeToTheMoon, 2009).

=1.18kg/m3

=0.95kg/m3

V=2200m3

m=? kg

If the starting temperature was lower than 25ᴼC then there would be greater lift because the difference between external and internal densities would be greater.

As clearly outlined earlier gas laws are very effective in explaining real life situations of a small scale, such as scuba diving and hot air balloons. However it must be kept in mind that gas laws deal with ideal gases and may not apply in other real life situations on a much bigger scale; situations such as global warming.

What is global warming?

Global warming is the gradual warming of the earth’s average surface temperature, due to greenhouse effect. Greenhouse effect is a natural process where some of the sun’s energy is trapped by greenhouse gases in the atmosphere, warming the earth enough to support life. Greenhouse gases are natural gases occurring in the atmosphere tuned to absorb infrared light. Major greenhouse gases include carbon dioxide, methane and nitrous oxide (WWF, 2007).