Applied Physics Topics 2 Dr Andrey Varvinskiy Consultant Anaesthetist Torbay Hospital, UK EDAIC Paper B Lead and Examiner Conflict of interest declaration WHAT DECLARATION Grants/research support/P.I. N/A Employee N/A Consultation fees N/A Honoraria N/A Speakers bureau N/A Company sponsored N/A Stock shareholder N/A Spouse/partner N/A Scientific Advisory Board N/A Other Flight and hotel funded by ESA www.esahq.org TOPICS 2 Gas Laws Other Laws: Dalton, Avogadro Critical temperature Critical pressure Solubility Diffusion www.esahq.org Boyle’s Law (Boyle-Mariotte law) PV=k1 For a fixed amount of an ideal gas kept at a fixed T, pressure and volume are inversely proportional (while one doubles, the other halves) www.esahq.org Cylinder content Air,O2,Helium: by pressure gauge as P is proportional to V N2O and CO2: by weight. Liquified under Pressure www.esahq.org Application of Boyle’s Law for calculating a content of a cylinder p1 x V1 = p2 x V2 P1 = Gauge pressure of cylinder V1 = Physical volume of cylinder P2 = Atmospheric pressure V2 =Actual amount of gas stored in the cylinder For CD O2 cylinder : 230 x 2 = 1 x V2 = 460 L www.esahq.org Charles Law Law of Volumes V/T = k2 Constant pressure Gases expand when heated www.esahq.org Charles Law Practical Application Heat loss from the body - air next to the body surface gets warmer and moves up Patient loses heat Important in paediatrics www.esahq.org 3rd Perfect Gas Law P/T = k3 Constant volume the absolute pressure of gas varies directly to its absolute temperature www.esahq.org 3rd Perfect Gas Law Practical Application Medical gases are in cylinders at constant volume and high pressures (138 Bar in a full O2 cylinder) At high T, pressure will rise causing explosions Molybdenum steel can withstand pressures to 210 Bar. Weakening of metal in damaged cylinders are at a greater risk of explosion due to rise in temperature. www.esahq.org The Universal Gas Law Combining all the gas laws together yields an important equation: the universal or ideal gas law. PV = nRT P – Pressure of gas V - Volume n = the number of moles of the gas T – Temperature of gas R = the universal gas constant www.esahq.org Standard Temperature and Pressure (s.t.p.) Volumes of gases are affected by T and P hence there is a need to specify those And to correct results 273.15 K (00 C) 101.325 kPa www.esahq.org Dalton's Law Of Partial Pressures in a mixture of gases the pressure exerted by each gas is equal to the pressure which would be exerted if that gas alone was present PressureTotal = Pressure1 + Pressure2 ...Pressuren www.esahq.org Dalton's Law Practical Application In anaesthesia the partial pressures of gases in a mixture are of interest By applying Boyle’s and Dalton’s law the partial pressure of a gas in a mixture is obtained by multiplying the total pressure by the fractional concentration of the gas. www.esahq.org Dalton's Law Practical Application In a mixture of gases where 0.05% - CO2, 20.9%- O2 and 78.1% - N2 If the total Pressure is 100kPa the pCO2 – 0.05kPa, pO2- 20.9kPA, pN2 – 78.1kPa If the total pressure doubles (200kPa) then the partial pressure of each gas doubles. www.esahq.org Avogadro's Hypothesis equal volumes of gases at the same temperature and pressure contain equal numbers of molecules www.esahq.org Avogadro's Hypothesis Because the molecular weights of gases differ, there will be a different mass of any gas in a given volume at the same temperature and pressure Therefore it is more convenient to express a quantity of a gas in terms of the number of molecules, rather than in terms of mass. www.esahq.org AVAGADRO and the MOLE A MOLE is the quantity of a substance containing the same number of particles as there are atoms in 0.012kg of carbon12 There are 6.022 x 1023 atoms in 12 g of carbon 12. This is called Avagadro’s Number One mole of any gas at s.t.p. occupies 22.4litres www.esahq.org The Mole THUS: 2g of Hydrogen 32g of Oxygen 44g of Carbon Dioxide All occupy 22.4 litres at s.t.p www.esahq.org Ideal Gas Law The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases www.esahq.org Critical Temperature T above which a substance cannot be liquefied however much pressure is applied N2O: 36.5C O2: -119C CO2: 31C “Gas” applies to a substance above its CT “Vapour” is for a substance below its CT www.esahq.org Critical Pressure Pressure needed to liquefy the gas at its critical temp N2O - 72 bar O2 – 50 bar CO2 – 73 bar www.esahq.org Filling Ratio mass of gas in a cylinder/mass of water which would fill the cylinder For N2O it’s 0.75 in the UK, hotter climates – 0.67 Necessary to prevent explosion in case of rise in temp So N2O cylinder contains a mixture of liquid and vapour www.esahq.org Solubility and Henry’s Law At particular T 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 different gases have different solubilities Overall: solubility of a gas depends on partial pressure, temp, gas and liquid concerned ↑temp of liquid =>↓dissolved gas www.esahq.org Partition Coefficients ratio of amount of a substance present in one phase as compared with another two phases must be of equal volume, specified temperature in equilibrium Tension is often used in place of partial pressure for gases in solution (don’t mix with surface tension) Could be applied to 2 different liquids (blood-gas, oil- gas) www.esahq.org Diffusion Movement of a substance from an area of high concentration to one of low concentration due to spontaneous random movement of its constituent particles Not an active process as no energy required www.esahq.org Fick’s law of diffusion rate of diffusion of a substance across a membrane is proportional its concentration gradient and inversely proportional to the tissue thickness diffusion of gas across a membrane or into or out of a liquid is proportional to the gas’s solubility in the liquid CO2is more soluble than O2 and so diffuses more rapidly across the alveolar membrane N2O more soluble than N2 - can diffuse into and expand closed cavities www.esahq.org Graham's Law Effect of molecular size Rate of diffusion of a gas is inversely proportional to the square root of the molecular weight Only applies to simple models and is inaccurate when dealing with complex biological membranes www.esahq.org Diffusion Summary Diffusion is proportional to the tension gradient D depends on area and thickness of membrane D is affected by molecular size (larger diffuse less rapidly) Liquids diffuse less rapidly than gases www.esahq.org QUESTIONS? Cross and Plunkett • www.esahq.org Title area First Name Last Name Department Hospital, Country.