Gas laws and its implications in Anaesthesiology

Gas laws in anaesthesia,its needs and Implications
By Dr.S.Sameer Ahmed,
JR1,
Department of Anaesthesia and critical care,
RRMCH Bangalore

1. AND ITS APPLICATIONS in ANAESTHESIOLOGY By Dr.Sharieff Sameer Ahmed Moderators ; Dr.Jyothi Dr.Sanath

2. Why Learn Gas laws as Anaesthesiologists? Gas laws and physics play a crucial role in our practice. They are needed in a wide variety of situations in the OT as well as the ICU For better induction of anaesthesia For appropriate use of Boyle's Machine To better understand the mechanics behind using Nitrous Oxide and volatile anesthetics To prevent Hazards in the hospital.

3. Common definitions

4. Gas It is a state of matter When at a cool temperature a clump of molecules might be so closely packed we may call it a solid. When heat is added,the molecules vibrate more and create more space giving rise to a liquid When the molecules gather up enough kinetic energy(The boiling point of said liquid) they might “break free” and end up in gaseous state

5. PRESSURE Pressure is the force exerted per unit of area P = F/A As gas molecules collide with the wall of the container holding it, they exert a net force, which when exerted over a certain area is defined as pressure 1Bar= 1 Atm = 100kPa = 760mmHg = 760torr = 14.7psi = 1000cm water Absolute pressure in cylinder= Gauge pressure+ Atmospheric pressure

6. Temperature Unit to measure heat,a form of kinetic energy generated by the movement of particles Units = O C = 32 F = 273K Absolute Temp. O K = -273 C

7. Critical Temperature Temperature above which a gas cannot be liquefied, No matter how much pressure is applied. N 2 O 36.5 C, O 2 - 119 C CO 2 31.1 o C Pseudocritical temperature is the gas mixture Temperature at which gas mixture may separate out into constituents

8. Ideal Gas A gas which o beys universal gas law PV= nRT at all temp & pressures Theoretical Negligible intermolecular forces collisions between atoms or molecules are perfectly elastic

9. Real Gas Real gases H 2 , N 2 , O 2 exhibit properties that cannot be explained entirely using the ideal gas law Behave like ideal gas at STP Air at atmospheric pressure is a nearly ideal STP = standard temperature and pressure

10. STP S tandard reference conditions as being 0 °C and 1 Atm/ 100  kPa (1 bar)

11. Gas laws Boyles’s Law Charle’s Law G ay Lussac’s Law Universal gas law Dalton’s Law of partial pressures Henry’s law Graham’s law for turbulent flow Reynolds’s number Bernoulli’s principle Venturi’s effect Coanda effect Poynting effect Hegan-Poissuilles law for laminar flow Raoult’s law Graham’s law of diffusion

12. BOYLE's LAW This law states that if the temperature is held constant, the volume of a given amount of gas will vary inversely with the absolute pressure.  V  1/ P or P V = constant ( k 1 )

13. APPLICATION OF BOYLE's LAW Consider a patient who needs high flow O 2 at 10L/min being shifted to a different hospital You have a 10L O 2 cylinder, with a gauge pressure of 19,900kPa How much time do you have on that O 2 cylinder?

14. Absolute pressure = G auge pressure + A tmospheric pressure Therefore, Using P 1 V 1 = P 2 V 2 (1 9 , 9 00 +100) x 10 = 100 x V 2 V 2 = 20,000  10 = 200 litres (10 litres will stay behind in the cylinder, so 199 litres are available for delivery at atmospheric pressure ) At 10 l/min  1 99 0/10 = 1 99 min 3 hours and 19 minutes

15. GAY Lussac LAW At a constant volume, the absolute pressure of a given mass of gas varies directly with the absolute temperature. P  T or P/T = Constant (k 3 )

16. APPLICATIONS of GAY Lussac LAW An O2 cylinder indicates a pressure of 132 atm while being transported in hot weather when the temp is 44C. What pressure will be indicated when it is placed in a cool operation theatre when the temp is 20C?

17. P1/T1=P2/T2 132/44=P1/22 P1= 132x22/44 P1=66

18. APPLICATIONS of GAY LUSSAC LAW If oxygen cylinder is kept under the sun its temperature increases and according to GAY LUSSAC’s law pressure is directly proportional to temperature, (volume being constant). Pressure increases inside the cylinder so much that the cylinder may even explode. Hence the oxygen cylinders should be stored in a cooler place. In order to prevent accidental explosion safety valves are incorporated in the cylinder valves.

19. APPLICATIONS of GAY LUSSAC LAW The Nitrous Oxide filling ratio is calculated as: weight of fluid in the cylinder/weight of water required to fill the cylinder Within a cylinder of gas, according to the GAY Lussac law, as the ambient temperature rises , the pressure inside the cylinder will also rise .

20. APPLICATIONS of GAY LUSSAC LAW This is important in the storage of nitrous oxide At room temperature, it is stored in a cylinder as a liquid, with vapour on top. As the temperature rises, the pressure exerted by the vapour , the Saturated Vapour Pressure, also rises. If this exceeds the pressure capacity of the cylinder, then it could explode, as the volume is constant.

21. APPLICATIONS of GAY LUSSAC LAW FRANGIBLE DISC has a diaphragm that breaks at a particular pressure. As the temperature inside the cylinder increases, the pressure also increases (GAY LUSSAC’S LAW)

22. AVAGADRO HYPOTHESIS Equal volume of gases at the same temperature and pressure contain equal number of molecules Based on the above hypothesis-one mole of a gas contains- 6.023 x10 23 molecules This law can also be defined as -One mole ( molecular weight) of any gas at STP occupies 22.4 litres of volume. When mole ( molecular weight) is expressed in grams it’s called as gram molecular weight.

23. So 1 gram molecular weight of any gas at STP, will contain 6.023x10 23 molecules and occupies 22.4 litres of volume. Standard temperature is 273 K and standard pressure is 760 mm of Hg.

24. APPLICATION OF AVOGADRO's HYPOTHESIS Calculation of the volume of nitrous oxide gas available from a cylinder A typical full nitrous oxide cylinder contains 3.4 kg of nitrous oxide. The molecular weight of nitrous oxide is 44 and so one mole is 44 g. If the measurements are made at s.t.p., what volume of nitrous oxide is obtained from this cylinder?

25. APPLICATION OF AVOGADRO's HYPOTHESIS 44 g (1 mol) nitrous oxide occupies 22.4 litres at s.t.p Therefore: 3400 g nitrous oxide occupies 22.4 x 3400/44 litres = 1730 litres By this principle, the weight of nitrous oxide is used to indicate how full the cylinders are. The weight of the empty nitrous oxide cylinder is known as the tare weight and is always stamped at the top. Consequently, by weighing the cylinder the nitrous oxide content may be calculated.

26. CHARLES' LAW It states that AT CONSTANT PRESSURE, VOLUME IS DIRECTLY PROPORTIONAL TO THE ABSOLUTE TEMPERATURE V  T or V /T is a constant

27. APPLICATION OF CHARLE'S LAW D etermination of the amount of vapour (volatile anaesthetics) at room temperature If 1ml halothane gives 207mL vapour at 273K how much vapour is present at 293K? V 1 /T 1 =V 2 /T 2 V 2 = 207x 293/273 =221mL vapour

28. APPLICATIONS OF CHARLE's LAW To calculate the cost of volatile anaesthetics By Avogadro Hypothesis, 168 ml of sevoflurane vapour is at standard temperature of 273 K, to calculate at room temperature,293 K, V1/T1= V2/T2 V1=168 ml T1=273 K V2=? T2= 293 K V2= V1 x T1 T2 V2= 168 x 293 = 180 ml 273 Thus 1 ml of sevoflurane at room temperature gives 180 ml of sevoflurane vapor

29. If 2% of sevoflurane is used with a fresh gas flow of 6 litres T hen every minute 120 ml of vapour will be used P er hour it will be 7200ml of vapour Since 1ml of liquid sevoflurane will give 180 ml of vapour , then 7200/180= 40 ml 40ml of the liquid sevoflurane will be used per hour . Since cost of 250 ml of sevoflurane is Rs. 7500 1 ml will cost Rs 30. Then 40 ml would cost 40x30= 1200 Rs .

30. THE UNIVERSAL GAS CONSTANT PV = Constant (k 1 ) Boyle V/T = Constant (k 2 ) Charles P/T = Constant (k 3 ) (3 rd Law) By combining the perfect gas laws with Avagadro’s hypothesis we arrive at the following equation: PV/T = Constant (k 4 ), for any given quantity of gas For any 1 mole of any gas, this constant (k 4 ) is the UNIVERSAL GAS CONSTANT – R

31. THE UNIVERSAL GAS LAW Therefore PV = n RT n is no. of moles of the gas R depends on the units.

32. APPLICATIONS OF UNIVERSAL GAS LAW The universal gas equation may be used to calculate the contents of an oxygen cylinder. Referring to the equation, in normal circumstances T is constant at room temperature, V is constant as the cylinder has a fixed volume, and R is by definition a constant. These terms therefore may be practically removed from the equation. P is directly proportional to n The gauge pressure (P) can thus be used to measure the amount of oxygen remaining in the cylinder (n).

33. Daltons Law of Partial Pressures Given by John Dalton . Dalton’s law of Partial Pressures states that in a mixture of gases, the pressure exerted by each gas is the same as that which it would exert if it alone occupied the cylinder

34. APPLICATIONS OF DALTON's LAW

35. APPLICATIONS OF DALTON's LAW

36. APPLICATIONS OF DALTON's LAW

37. JOULE THOMPSON EFFECT Also known as ADIABATIC CHANGE The three gas laws describe the behaviour of a gas when one of the three variables (P/V/T) is constant. If these conditions are applied, heat energy must be added or taken from a gas if it changes pressure or volume The state of a gas can however be changed without allowing the gas to exchange heat energy with it’s surroundings That is,t he heat is retained within the system.

38. APPLICATIONS OF JOULE THOMPSON's EFFECT T he theoretic hazard when high pressure pipelines are opened into a low pressure anaesthetic machine, without regulator valves. The rapid pressurization is associated with a local large temperature rise, and risk of fire and explosion Cylinder should be opened slowly as rapid opening of the valve will produce a rapid flow of oxygen into the space in the tubing of the yoke assembly and the pressure regulator

39. APPLICATIONS OF JOULE THOMPSON's EFFECT This produces a rapid compression of oxygen in the narrow tube producing a very high temperature leading to possible explosion . Hence oxygen cylinder should be opened slowly to prevent adiabatic process

40. POYNTING EFFECT W hen two gases, one of high and another of low critical temperature are mixed in a container, the critical temperature of the gas with a high critical temperature will decrease to a lower level (pseudo critical temperature) and the mixture will remain as a gas above this pseudo critical temperature.

41. APPLICATION OF POYNTING EFFECT Entonox 50% O 2 50% N 2 O The critical temperature of oxygen is -118 ° C and of N2O is 36.5 ° C. when these gases are mixed in a same cylinder, then the critical temperature of the mixture will be -6° C due to POYNTING EFFECT and the mixture will remain as gas at room temperature.

42. Critical Temperature Temperature above which a gas cannot be liquefied, No matter how much pressure is applied. N 2 O 36.5 C, O 2 - 119 C CO 2 31.1 o C Pseudocritical temperature is the gas mixture Temperature at which gas mixture may separate out into constituents

43. In cold climates if the temperature is less than -6 ° C, then N2O will separate into its liquid form and will remain in the bottom of the cylinder and the patient will get only O2 initially and hence will not produce any analgesia. Later patient gets only N2O which can result in hypoxia. Hence in such situation cylinder should be thoroughly shaken before use. APPLICATION OF CRITICAL TEMPERATURE

44. COANDA EFFECT It is the tendency of the fluid jet to be attached to a nearby surface. This phenomenon is also called as wall attachment. When a narrow tube encounters a Y junction of the wide bore, because the flow tends to cling to one side, the flow will not evenly divide between the two outlets, but flows through only one limb of the Y piece. This behavior is called COANDA EFFECT.

45. APPLICATION OF COANDA EFFECT A valve mechanism with no moving parts can be made if two tubes are inserted at each side at the exit of the narrow tube. Flow through either of these side tubes can switch the main flow from one exit tube to the other. Having been transferred, the flow continues into the appropriate branch after the switching flow has been removed.

46. APPLICATION OF COANDA EFFECT Du e to COANDA EFFECT ,if there is narrowing before the branching, t he pressure drops, the velocity of the air increases . B ut the flow tends to cling to one side & doesn’t d ivide evenly between the branches resulting in unequal gas flow to the alveoli. Mucus plug at the b ranching of tracheo-bronchial tree may cause maldistribution of respiratory gases

47. Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.

48. ROULT's LAW Raoult’s law states that the reduction of vapour pressure of a solvent is proportional to t he molar concentration of the solute. APPLICATIONS This law is useful during calculation of concentrations o f volatile anaesthetics in azeotropic mixtures.

49. HEGAN- POISSUILLES’ LAW FOR LAMINAR FLOW States that , “ for a viscous fluid which moves with laminar flow through a cylindrical conduit of radius r and length L, the volume flow rate Q is directly proportional to the pressure difference Δ P between the two ends of the conduit and to the fourth power of its radius, and inversely proportional to the viscosity ƞ of the fluid and to the length of the conduit” Q = π r4 (P1 – P2) 8 ƞ L

50. REYNOLDS NUMBER It can be predicted if the flow of a fluid through a conduit would be laminar or turbulent (i.e., with chaotic changes in pressure and speed) using the so-called Reynolds number.(Re) Reynolds number =  d/   = Linear Velocity of fluid  = Density of fluid d = Diameter of tube  = Viscosity of fluid

51. This equation tells us that turbulent flow occurs when fluids flow at high velocity , through large diameter tubes and when fluids are relatively dense . Density is much more important than viscosity when it comes to turbulent flow . Density : The mass of substance occupying a unit volume, Viscosity : A measure of its resistance to gradual deformation by shear or tensile stress .

52. Measurements have shown that when: Reynold’s number <2,000, there is likely to be laminar flow; Reynold’s number 2,000–4,000, there is likely to be transitional flow (laminar and turbulent); and Reynold’s number >4000, there is likely to be turbulent flow.

53. APPLICATION OF REYNOLD's NUMBER Use of HELIOX (Helium and Oxygen mixture) E ffect of density on the onset of turbulent flow is the use of helium in respiratory disorders. H elium reduces the density of gas inhaled Reynolds number =  d/  Hence makes flow more laminar and reducing resistance.

54. GRAHAM's LAW OF FLOW Flow = √ P1-P2 √ density Since flow α 1/ resistance, above equation can also be rewritten as Resistance = √ density √ P1-P2

55. APPLICATION OF GRAHAM's LAW OF FLOW Use of HELIOX (Helium and Oxygen mixture) E ffect of density on the onset of turbulent flow is the use of helium in respiratory disorders. H elium reduces the density of gas inhaled Resistance = √ density √ P1-P2 Hence Lowers resistance to airflow

56. APPLICATION OF GRAM'S LAW OF FLOW W henever there is tracheal stenosis the flow of gases will be turbulent . H ence there will be increase in the resistance and decreases flow across the stenosis . Flow and resistance will depend on the density of the gas as per GRAHAM’S LAW. Mixture of oxygen and helium will have a decreased density compared to O2 or air . H ence using HELIOX will decrease the resistance and increase the flow.

57. HENRY's LAW Henry's law states that at a particular temperature the amount of a given gas dissolved in a given liquid is directly proportional to the partial pressure of the gas in equilibrium with the liquid. At constant Temperature, Amount of gas dissolved ∝ Partial pressure of the gas in the liquid

58. APPLICATIONOF HENRY's LAW The effect of high pressure on the solubility of nitrogen is particularly relevant to deep-sea divers as nitrogen and other gases, if breathed under pressure, pass into solution in the tissues. If a return to atmospheric pressure is made too rapidly, the nitrogen comes out of solution as small bubbles in the joints and elsewhere, giving rise to the condition known as decompression sickness or the 'bends'.

59. APPLICATIONS OFHENRY's LAW Hyperbaric chambers These are used for Hyperbaric oxygen therapy in clinical use. They intend to treat Anemia (Increases partial pressure of Oxygen in blood by so as to allow more diffusion into the blood) Decompression sickness (Increases the pressure so that gas bubbles of Nitrogen may get reabsorbed into the blood stream and then the pressure is slowly tapered down)

60. Air embolisms Crush injury E ffects on peripheral oxygen transport, muscular ischemic necrosis, compartment syndrome, and infection prevention

61. APPICATION OF FLOW LAWS Consist of a vertical tapered glass tube containing a ball or bobbin which floats on the stream of gas. At low flow rates , the tube is narrower and under these circumstances, flow is laminar and respects the Hagen Poiseuille equation. At higher flow rates, the bobbin moves up the flowmeter until it acts like an orifice and flow becomes turbulent . In this situation the density of the gas affects flow, and hence calibration is gas- or agent-specific . Graham's law of flow. Flow in this situation becomes proportional to the square root of the pressure and so the graduations on the flowmeter are not uniform

62. Application : As long as gas flow through an endotracheal tube is laminar, the larger the tube, the less resistance there is to flow . This may be relevant when patients are breathing spontaneously via an endotracheal tube because a narrower tube will increase the work of breathing . Anaesthetic breathing circuits are designed to maintain laminar flow as much as possible , and reduce the work of breathing for spontaneously ventilating patients . Connections are kept straight, if possible, as acute angles can cause turbulent flow . Also, unnecessarily long circuits will reduce flow.

63. FICK's LAW OF DIFFUSION

64. APPLICATION OF FICK's LAW OF DIFFUSION Gas exchange in the alveoli. Exchange increased with excersice and breathing exercises as it increases the surface area of the alveoli by helping it expand. Exchange reduced in fibrotic lung diseases,smoking where in the alveolar damage reduces the surface area

65. BERNOULLI's PRINCIPLE Bernoulli’s principle : A gas flowing through a tube encounters a constriction, at that point the pressure drops and the velocity increases i.e. kinetic energy increases .

66. High pressure to intermediate pressure to Low pressure system Increases velocity decreases pressure

67. VENTURI EFFECT Entrainment of air from the surrounding due to fall in pressure at the point of constriction is called as VENTURI’S EFFECT .

68. When rise in velocity at the constriction can be so high that it fluid’s lateral pressure may fall below atmosphere pressure – negative If there is an open tube distal to the constriction this negative pressure pull another fluid into the primary flow- fluid entrainment. Entrainment ratio= Entrained flow/Driving flow.

69. APPLICATION OF VENTURI EFFECT In a nebuliser, gas as the driving fluid enters by the centre tube ,entrains liquid from a side tube and breaks into smaller droplets suitable for inhalation.

70. Uses of Venturi Principle MEDICAL USES fixed % oxygen delivery systems jet ventilators modern vaporizers nebulization chambers suction apparatus NON-MEDICAL USES spraying perfumes / paints sand blasters foam fire extinguishers petrol carburettors others : pethick’s test for patency of bains circuit

71. THANK YOU