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Effects Of Pressure and Gas Laws | Under Compressibility Of Gases

GAS LAWS AND EFFECTS OF PRESSURE 

Because gases are compressible, their volumes can be altered by a change in pressure. The amount by which the volume changes depend on the change of pressure and are explained fully in Boyle’s Law. 

Gas Laws 

1. Boyle’s Law. ‘For a fixed mass of gas at a constant temperature, the volume will vary Inversely as its absolute pressure.’ 

Formula:

Pressure (bar abs) x Volume (Any Unit) = Constant 

P₁ x V₁ = P₂ x V₂ 

From this law, it follows that the density varies directly from the absolute pressure. In other words, if the pressure of a gas is doubled the density is also doubled, but the volume is decreased to one-half of the original volume. It is most important that the diver should clearly understand the relationship between volume and pressure.

2. Pressure Law.

It is not necessary to complicate this simple rule by taking into account the exact effect of temperature changes, but it should be observed that if the temperature of a confined gas is increased there will be a resultant rise in pressure and if the temperature is decreased there will be a corresponding fall in pressure. Alternatively, if the pressure of gas in a container is increased by compression there will be a temporary rise in the gas temperature, and if the pressure is reduced there will be a temporary fall in temperature. 

The extent of this temporary rise or fall in temperature will depend upon the rate at which the pressure is increased or decreased. The higher the rate of increase or decrease in pressure the greater will be the corresponding rise or fall of temperature.

pressure-law-diving-skeleton
pressure-law-diving-skeleton

PRESSURE LAW STATES

‘For a fixed mass of Gas at Constant Volume, the Absolute Temperature is directly proportional to the absolute pressure’. 

Formula:

Pressure (bar abs)/ Temperature (K) = Constant 

P₁/T₁ = P₂/T₂

❕Note. Absolute Temp (k) = °C + 273k (Kelvin)

3. Charles Law.

This law states that the volume of a given mass of gas at constant pressure is directly proportional to the absolute thermodynamic temperatures; equivalently, all gases have the same coefficient of expansion at constant pressure. This is approximately true at low pressures and sufficiently high temperatures as the ideal gas behavior is appreciated. This is also known as Gay-Lussacs Law.

CHARLES LAW STATES 

For a fixed mass of Gas at a constant pressure, the volume is directly proportional to the Absolute Temperature.

Charles-law-diving-skeleton
Charles-law-diving-skeleton

i.e        V₁/T₁ = V₂/T

❕Note. Absolute Temp = °C + 273 K (Kelvin)

Examples: What is the volume of a 1-liter sample of hot gas after passing through a constant-pressure cooling coil which reduces the temp from 56°C to 24°C?

V₁/T₁        =    V₂/T

156+273 =    V224+273

V2              =    [297/329]

V2              =    0.902 liters 

Examples: Between 2 stages of an air compressor 10 liters of gas initially at 30°C reduces in volume to 9.87 litres. What is the temp of gas after cooling in °C? 

V₁/T₁ = V₂/T

V1       = 10            T1 = 30+273

V2       = 9.87         T2 = C + 273 

10/30+273 = 9.87/°C+273

°C +273       = 9.87 x (30+273)/10

°C                = [9.87 x 303/10]-273

°C                = 26.06

Compressibility of Gases
  • For theoretical purposes it has been established that gases at low density closely follow Boyle’s Law and the Pressure Law, however, these equations are only strictly true for ideal gases, and even then only at low densities.
  • The point at which a gas deviates from an ideal state is dependent on temperature and pressure and forms what is known as a compressibility factor which must be applied to conventional gas calculations.
  • At high pressures (above 275 bar), the molecules within a gas are forced to interact differently, thus changing the properties of the gas from its ideal state.
compressibility-of-gases-diving-skeleton
compressibility-of-gases-diving-skeleton
  • Therefore, when considering the contents of gas flasks such as the diluent and bail-out pressure vessels containing an Oxygen/Helium mixture, this effect must be taken into consideration. This has the result of giving a lower figure for gas content than would be expected from conventional gas calculations.
  • When filled with 16% Oxygen, and 84% Helium, the 2.87 liters diluent flask of the diving set has a nominal capacity of only 939 liters at the working pressure of 345 bar and not 993 liters as expected. When filled with the same gas, the 1.5 liters bailout cylinder has a nominal capacity of 491 liters at the 345 bar working pressure, not 519 liters.
Conclusion: 

Understanding gas laws and pressure effects is crucial for practical applications, ensuring safety and accuracy in calculations. By grasping gas laws, and pressure effects, and accounting for deviation, accurate calculation and safe applications can be achieved.

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