FRCA Physics

Second

(a measure of time – s)

One second = 9,192,631,770 oscillations of a Caesium 133 atomic clock.

Metre

One metre = The distance travelled by light in vacuum in 1/299,792,458 second

Mole

(a measure of amount of substance – mol)

One Mole = The amount of substance containing the same number of atoms/molecules as there are atoms in 12g of Carbon-12

0.012kg of carbon-12

Ampere

One Ampere = The current applied to two parallel conductors of negligible cross section and infinite length, one metre apart in a vacuum which would produce a force between them of 2.0 x 10-7 Newtons per metre.

current needed to produce a certain electromagnetic force between two conductors one metre apart

Candela

(a measure of light – cd)

One Candella = The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×10¹⁴ hertz and that has a radiant intensity in that direction of 1/683 watt per square radian.

amount of light that supplies a certain intensity of light energy

Kilogram

One Kilogram = The mass of the international kilogram prototype in Pavillon de Breteuil, Sévres, France.

Kelvin

(a measure of temperature – K)

One Kelvin = 1/273.16 of the thermal energy of the triple point of water.

triple point of water

T=273.16K (0.01^∘C), P≈611Pa

three phases: gaseous, liquid, ice

absolute zero

0 K= −273.15^∘C

Newton

Unit of Force – kg.m.s^-2

Pascal, Pressure

Unit of pressure – 1N/m² = kg.m^-1.s^-2

Pressure = Force applied per unit area

Joule

unit of Energy – kg.m^-2.s^-2

1 J to praca wykonana przez siłę 1 N działającą na odległości 1 m.

STP, Standard temperature and pressure

0^oC (or 273.15K) and atmospheric pressure or 101.325 kPa (760 mmHg, 1 Bar).

Boyle's law

at a constant temperature in a closed system with a fixed mass of gas, the pressure is inversely proportional to the volume
P=1/V (temperature constant) Water ‘boyles’ at a constant temperature.

P x V = K (constant)
if the piston is driven inwards to halve the volume then the pressure doubles (P1V1 = P2V2)

Charles's law

at a constant pressure in a closed system with a fixed mass of gas, the volume is directly proportional to the absolute temperature
(V ∝ T)

Charles is under constant pressure to be king.

Gay Lussac’s Law

At constant volume, Pressure of a fixed volume of gas will increase in proportion to absolute temperature
(P ∝ T) or P / T = K (constant)

Ideal gas law

PV=nRT

P = Pressure in Pascals (NOT kPa!!)
V = Volume in m3
n = number of moles
R = Molar gas constant 8.31 J/K/Mol
T = Temperature (in Kelvin!)

Henry's Law

the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas on the surface of the liquid
(dissolved gas ∝ P)

=At constant temperature, the amount of gas dissolved in a liquid is directly proportional to the partial pressure of this gas in equilibrium with it.

At constant pressure: increasing temperature decreases gas solubility

Dalton's law

Total pressure of a gas is equal to the sum of the partial pressure of the component gases

Force

Force = mass x acceleration (kg m s^-2 or N)

Work

Work = force x distance (Nm or Joules)

Work = pressure x volume (Nm^-2 x m³ = Nm or Joules)

Work = 1/2mass x velocity² (stopping the car)

Work = mass x specific heat capacity x temp. change

Power

Power = work done per second (W, J/s)

Flow

• Movement of a volume of fluid from one place to another per unit time

• m3/s, L/min.

• Flow is represented by the equation: Flow = Quantity/Time

Viscosity

Viscosity (η) is the tendency of a fluid to resist flow or, to put it another way, 'fluid friction'. It is measured in poise (P) or Pascal seconds (Pa.s). For example, blood runs slower than crystalloids through a giving set as blood has greater viscosity

viscosity is the most important factor affecting laminar flow

Newtonian and non-newtonian fluids

• Newtonian, e.g. water or air - where viscosity is constant, or

• Non-Newtonian, e.g. blood - where viscosity is not constant

Density

Density is the mass of substance per unit volume.

Density is measured in kilogram per metre cubed (kg/m³) and is usually denoted by the Greek letter 'ρ'.

is the most important fluid factor for turbulent flow

Hagen-Poiseuille equation

for laminar flow

Turbulent flow

Turbulent flow ∝ r2 and √∆P and 1/length and density of the fluid

• Flow ∝ r²
  Larger radius → much greater flow, but less increased than laminar

• Flow ∝ √ΔP
  Increasing pressure increases flow, but not linearly

• Flow ∝ 1/√ρ
  Lower-density gases flow more easily in turbulence (e.g. Heliox).

• Flow decreases as tube length increases
  Longer tube → more resistance → less flow.

Heliox and flow

Heliox has a low density, which reduces turbulent resistance and makes airflow easier, for example in upper airway obstruction (predominant turbulent flow)

In bronchospasm (lower airway obstruction), airflow is predominantly laminar, where resistance depends mainly on viscosity rather than density. Since the viscosity of heliox is similar to that of air, heliox is less beneficial in bronchospasm

Reynold's number (Re)

• Re <2000 flow is likely to be laminar

• Re >2000 flow is likely to be turbulent

• ρ = fluid density

• v = fluid velocity

• d = tube diameter

• η = fluid viscosity

So, the critical velocity = Reynold's number = 2000. Transition from laminar to turbulent flow depends on the gases present

Resistance

Laminar flow resistance

Turbulent flow resistence

Resistance increases with flow in turbulent flow

Bernoulli's principle

increase in velocity of an ideal fluid undergoing laminar flow is accompanied by a simultaneous reduction in its pressure

For an ideal fluid, that is non compressible, non viscous and flowing in a laminar fashion, the sum of the pressure, kinetic and potential energies per unit of fluid remain constant at all points

Venturi effect

When fluid moves through a tube with a constriction, the kinetic energy increases but at expense of a drop in pressure and potential energy past the constriction. This is used to entrain a second fluid/gas.

Coanda effect

Coanda effect describes the tendency of a stream of fluid flowing close to a convex surface to follow the line of the surface, rather than its original course

Rotameter

constant pressure, variable orifice flow meter

accurate to within 2% of the flow rate shown

• Needle valves with integrated flow control knobs

• Inverted conical tubes with calibrated markings

• Bobbins

low flows, the bobbin is at the narrower end of the tube. This means that the gas flows across an obstruction of greater length than diameter, i.e. the gas will behave as if flowing through a tube and flow will be laminar

high flows, the bobbin rises higher, into the wider portion of the tube. This means that the obstruction caused by the bobbin has greater diameter and reduced length, i.e. the gas behaves as if flowing through an orifice and flow is turbulent.

pneumotachograph

creates laminar flow through multiple small diameter tubes or mesh and uses the linear relationship between flow and pressure difference as per the Hagen- Poiseuille equation. The small resistance offered by the tubes causes a pressure drop proportional to the flow which is then transduced

Why are rotameters gas specific?

Because gases have different densities and viscosities, which in turn affect flow under different conditions.

What factors might affect the density or viscosity of a gas and have an effect on a rotameter's accuracy?

• Warmer gas has a lower density and viscosity, which may cause over-reading

• Reduced atmospheric pressure reduces the density of a gas, which may cause over-reading (though viscosity is unaffected by pressure)

critical velocity

critical velocity occurs at a Reynold's number of 2000, so the likelihood of turbulence depends on fluid density, viscosity, velocity and tube diameter.

Divers and nitrogen

When a deep sea diver breathes nitrogen under pressure, more nitrogen dissolves in the blood and tissues. In the event of a rapid ascent to atmospheric pressure, bubbles of gas can come out of solution and cause the syndrome known as 'the bends'

Fluid warmer and gas solubility

When cold fluid or blood passes through a fluid warmer, dissolved gas escapes and can appear as bubbles in the line. Therefore, many fluid warmers have a bubble trap in the warm limb to collect this gas.

Nitrogen and nitrous oxide solubility

Using nitrous oxide in patients with an air-filled cavity (such as a pneumothorax) can lead to an increase in cavity size, because nitrogen diffuses out more slowly than nitrous oxide enters.

Gas solubility

measured as the volume of gas that dissolves in a given volume of liquid, and is referred to as a solubility coefficient

Bunsen Coefficient

volume of gas, corrected to Standard Temperature and Pressure (STP), that dissolves in 1 unit volume of the liquid at the temperature concerned, where the partial pressure of the gas above the liquid is 1 atmosphere

Ostwald coefficient

• volume of gas that dissolves in 1 unit volume of liquid at the temperature concerned

• not corrected to STP

• independent of pressure, provided the dissolved volume of gas is measured at ambient pressure

partition coefficient

ratio of the amount of substance present in equal volume phases of liquid and gas in a closed system at equilibrium at a standard pressure and temperature

F_A/F_I ratio for various anaesthetic agents

1 osmole

contains Avogadro's number of particles (6.02 x 10²³)

plasma osmolarity

2 x (Na⁺ + K⁺) + urea + glucose

2 x because of associated anion (mainly chloride)

The Four Colligative Properties

As the number of particles in solution (osmolarity) increases:

• Osmotic pressure increases

• Freezing point decreases

  • ❄ harder to organise → freezing point ↓

• Boiling point increases

  • 🔥 harder to escape → boiling point ↑

• Solvent vapour pressure decreases (Raoult's Law)

• fewer escape → vapour pressure ↓

Isotonic and isosmolar

Molarity refers to the number of osmoles in solution whereas tonicity refers to the effective osmoles in solution (not glucos, urea, alcohol)

Moles and freezing temperature

One mole of a substance added to one kilogram of water depresses the freezing point by 1.86^oC.

Specific heat capacity

the amount of heat required to raise the temperature of a unit mass of substance by 1K (J/Kg/K)

Triple point water

temperature and pressure at which the solid, liquid and gas phases of a substance exist in equilibrium (for H₂O 273.16 K – 0.01°C, 611.2 Pa)

Latent heat

energy required to change the state of a substance without changing its temperature

Latent heat of vaporisation and fusion

Latent heat of vaporisation: heat energy required to convert a given mass of liquid into vapour whilst maintaining the same temperature

Latent heat of fusion: heat energy required to convert a given mass of solid into liquid at the same temperature.

Resistance wire (= resistance thermometer)

• The resistance of metal (e.g. platinum) increases linearly with temperature

  • the metal atoms vibrate more,

  • electrons collide with them more often,

  • so it becomes harder for current to pass

• A Wheatstone bridge is used to increase sensitivity

  Advantages	Disadvantages
  Very accurate	Fragile
  	Slow response time

Thermistor

• A small bead of metal oxide (semiconductor). Resistance falls exponentially with temperature

• Often used with Wheatstone bridge

• Used in PA catheter and oesophageal probe

  Advantages	Disadvantages
  Cheap	Calibration error*
  Fast response time	Deteriorate over time
  Small

Thermocouple

• Measures voltage

• Utilizes the Seebeck effect, when the junction is heated, it generates a small voltage.

• The circuit requires two junctions – the reference junction is kept at a constant temperature, a near-linear curve of voltage against temperature is produced at the other, measuring junction

Advantages	Disadvantages
Can be made very small	Needs signal amplification
Cheap
Tough

Liquid expansion

change in volume of a liquid dependent on the temperature:

• Mercury and alcohol can be used

• Mercury is more suitable for high temperatures -39°C and 250°C

• Alcohol is cheap, less toxic and more suitable for low temperatures between -117°C and 78°C

Advantages	Disadvantages
No power supply needed	2-3 min needed for equilibration
Simple	Risk of cross infection (non-disposable)
Reliable	Rigid - risk of breakage/trauma

Bimetallic strip

• Two dissimilar metals with different coefficients of expansion are fixed together in a coil. As the temperature rises the metals expand by different amounts causing the coil to tighten and the lever to move clockwise over the scale

• Used in thermostat switches

Bourdon (aneroid) gauge

Same principle (bimetallic strip) as when used for measuring pressure but the hollow tube is filled with a volatile liquid which expands as the temperature rises, causing the tube to unwind which moves a pointer

Tympanic and infrared ear thermometers

• Tympanic membrane emits electromagnetic (primarily infrared) radiation. The intensity and the wavelength for which the intensity of radiation is maximum varies with body temperature

• Infrared ear thermometers detect radiation emitted by the ear drum and ear canal

• Tympanic membrane thermometers are inserted further into the ear and receive radiation from the tympanic membrane only – more representative of core temperature

• Require two sensors- a pyroelectric sensor and a thermopile sensor (made of thermocouples)

Temperature measurement sites

Oesophageal	Accurate if lower 1/3 used – higher in the oesophagus the temperature may be cooled by inspired air
Rectal	0.5-1°C higher than core due to bacterial fermentation and insulating effect of faeces. Risk of perforation in babies
Blood (via PA catheter)	Best estimate of core temperature but very invasive
Skin	The difference between skin and core temperature can be used as an assessment of the degree of shock/peripheral perfusion
Bladder	High flow rates required for accuracy
Tympanic membrane	Correlates best with hypothalamic temperature

Heat loss during anaesthesia

• Radiation (40% of heat loss during anaesthesia is via radiation)

• Convection (30%)

• Evaporation (20%)

• Conduction (<5%)

• 10% is lost via respiration (heating of air plus latent heat of vaporization to humidify)

Radiators Catch Every Cold Lung

Radiation

Differs as does not require matter for heat transfer (the method the sun heats the earth). All objects >0 Kelvin emit radiation as electromagnetic waves. The overall amount of radiation emitted and absorbed by an object is a function of the temperature of the object. Accounts for 40% of the body’s heat loss in theatre.

Electromagnetic waves falling in the infrared spectrum are felt as heat.

Stefan-Boltzmann law

relates the total amount of radiation emitted as a function of its temperature:

E = sT⁴

E = the total amount of radiation emitted per m2 of an object

s = a constant

T = the temperature in Kelvin of the object

Conduction

• Heat transfer due to collision of molecules of two substances with differing temperatures. Molecules of the substance with higher temperature have a higher kinetic energy and collide with molecules of lower temperature with lower kinetic energy.

• Not an important method of heat loss in theatre

Convection

The transfer of heat by the movement of a liquid or gas itself (the air layer adjacent to the body is warmed by conduction, expands, becomes less dense and rises, carrying heat away)

Evaporation

Conversion of a liquid to the vapour state by the addition of heat which provides the energy to the liquid molecules to break the bonds between them. (Loss of this latent heat of vaporization due to evaporation of moisture on the skin surface causes cooling)

heat losses through respiration

humidification (8%) and warming (2%) of the inspired gases. This occurs through the combination of the other 3 processes

Reduced Heat Production

Basal metabolic rate

• GA → fall in basal metabolic rate → reduces heat generation by metabolically active tissues such as the liver

Spontaneous respiration

• NMBs and high dose opioids obtund spontaneous respiration in the patient and this reduces heat generation by respiratory muscle contraction.

Resting muscle tone

• All resting muscle tone is reduced which also reduces heat production.

Physiological response to hypothermia

• impaired moving or shivering, vasoconstriction and piloerection

• Behavioural responses

• The normal behavioural responses, such as finding a warmer environment and dressing appropriately, are removed.

Effects of Hypothermia

• Less volatile needed (i.e. reduced MAC)

• Prolongs effects of neuromuscular blocking agents

• Reduced metabolic rate (can be useful)

• Diuresis (secondary to inability to reabsorb sodium and water)

• Shivering causes postoperative O₂ consumption to increase up to 10x

• Coagulopathy; the clotting cascade is enzymatic and platelet function is temperature dependent

• Increased incidence of wound breakdown and infection

• Metabolic acidosis

NICE guidelines perioperative temperature regulation

• Higher risk if 2 or more of:

  • ASA 2 or above

  • Preoperative temperature <36°

  • Combined RA and GA

  • Intermediate or major surgery

  • At risk of CVS complications

• Need forced air warming if higher risk or surgery >30 min

• Temperature should be measured every 30 min

• IV fluids >500 ml should be warmed

absolute humidity

The mass of water vapour present per unit volume of gas at a given temp and pressure (mg/L or kg/m³)

Relative humidity

Absolute humidity/the SVP of water at that temp, or,

The ratio of the mass of water vapour in a given volume of air compared with the mass that would be required to saturate that given volume of air at the same temp.

Dew point

The temperature at which the relative humidity of the air exceeds 100% and water condenses out of the vapour phase to form liquid.

Hair hygrometer

• Measures relative humidity

• As relative humidity increases, the length of the hair increases which moves a pointer (human or animal hair or paper)

• Simple, most accurate between relative humidities of 30-90%

• Time lag between change in humidity and change in reading (approx 5 mins)

• Unreliable when ambient temperature below freezing

Wet and dry bulb hygrometer

• Relative humidity can be calculated

• Consisits of two mercury thermometers. One reads the ambient temperature whilst the second sits in a container of water which cools as the water evaporates due to loss of the latent heat of vaporization

• The rate of evaporation varies with the humidity of the surrounding air and hence the difference in temperature measured by the two thermometers varies as humidity varies

• Tables are used to determine the relative humidity for a given temperature difference

• Requires adequate air movement to be accurate

Regnault's hygrometer

• Relative and absolute humidities can be calculated

• Consists of a silver tube containing ether

• Air is bubbled through the ether-containing tube, cooling it

• When condensation occurs on the outside of the tube, this is the dew point (ie the temperature at which the ambient air is fully saturated)

• Graphs of water content of saturated air against temperature can then be used to determine relative humidity

• More accurate than either the hair hygrometer or the wet and dry bulb hygrometer

Normal humidity values

At sea level, 20°C, SVP = 17 g/m3

At sea level, 37°C, SVP = 44 g/m3

Upper airway 34°C, SVP = 34 g/m3

Dry air in the airways

• Drying of the respiratory mucosa

• Thickening of mucus causing airway plugging

• Reduced ciliary activity

• Keratinization and ulceration of the airways

Humidity in theatres

Should be maintained at 50-60% humidity

• Higher values are uncomfortable for staff

• Lower values will increase the patient’s heat loss via evaporation

• Lower values increase the risk of sparks due to the build up of static charge

methods for humidifying inspired gases

1. Cold water bath (passive)

2. HME

3. Hot water bath

4. Bernoulli (gas driven) nebulizer

5. Ultrasonic nebulizer

(least to most efficient)

Heat and moisture exchanger (HME)

• Two ports (one 15 mm, one 22 mm) +/- sampling port for gas monitoring; main body which contains a hygrophobic or hygroscopic (readily absorbs moisture) medium (ceramic fibre, paper, aluminum)

• As warm, humidified gas is exhaled, it condenses on the cooler HME and warms it. During inspiration gases pass through the HME the other way, the condensed water evaporates, humidifying the inspired air which is also warmed as it passes through the HME and is returned to the patient, warming and humidifying them. Heat is conserved during expiration and inspired air is heated and humidified

• humidifying efficiency of HMEs decreases with large tidal volumes

• Mostly consist of hygroscopic material e.g. foam or chemically coated paper

• Increase resistance 0.1-2 cm H₂O

• Can achieve a relative humidity of 60-70%

• Max: 35g/m3

Hot water bath

• Gas is passed over or through hot water

• The gas is not saturated at the temperature of the bath but as it cools along the tubing to the patient, gas becomes near saturated i.e. 100% humidity

Potential risks	Minimized via:
Condensation of water in tubing obstructs air flow	Heating the tubing Use of a water trap
Excessively hot gases	Use of a thermostat
Spillage of water into patient’s airway	Keep water level below that of the patient
Infection risk e.g. pseudomonas	Use containers prefilled with sterile water High temperature of the water

Nebulizers

produce microdroplets of water (or drug) suspended in a gas. The quantity of water droplets delivered is not limited by gas temperature as it would be with vapours.

Nebulizer size of droplets

The size of the droplets affects where they are deposited (ideal size 1-5 μm):

• 20 μm: deposited in tubing/upper respiratory tract

• 2-5 μm: tracheo-bronchial tree

• 1 μm: alveoli – may impair gas exchange

• <1 μm: no significant deposition – get inhaled and then exhaled again

Nebulizers types

• Gas driven: high flow gas is ejected close to the exit of a tube filled with water. This causes a drop in pressure (Bernoulli effect) and brings up water. The steam then hits an anvil to divide the droplets: 50-60g/m3

• Ultrasonic: Water is dropped onto a vibrating plate at ultrasonic frequency where tiny droplets are produced <2 μm, 80-90g/m3

• Risk of overhydration (can produce gas with 200% relative humidity at 37°C)

Methods for measuring humidity

• Relative

  • Hair hygrometer

  • Wet and dry bulb hygrometer

  • Regnault hygrometer

• Absolute

  • Transducer: change in either the resistance or the capacitance of a substance when it absorbs water vapour from the atmosphere

  • Mass spectrometer

• Other methods

  • Ultraviolet light absorption (reduction in transmission of UV light when water vapour present)

critical pressure

minimum pressure required to liquefy a gas at its critical temperature

Gas

When above the critical temperature, a reduction in volume will increase gas pressure. The substance is referred to as a gas (fixed gas).

A compressible fluid where intermolecular spacing is so large that intermolecular forces are negligible.

vapour

A gas below its critical temperature, thus compression to the liquid is possible.

When below the critical temperature, a reduction in volume will cause substance

liquidation.

vacuum insulated evaporator (VIE)

• double-skinned steel tank;

• a vacuum of 0.16-0.3 kPa → helps to maintain the oxygen at around -160°C to -180°C

• O2 below its critical temperature of -118° C → liquid form with a saturated vapour at a pressure of 10 bar above the liquid

• requires a cooling system: if none is used, temperature rises → increased pressure via third gas law and oxygen blows off through the safety valve (1500kPa) which also reduces temperature through latent heat of vaporisation

• supply pressure 4.1 bar

Nitrous oxide isotherms 40°C line

• This line is well above the critical temperature

• Above critical temperature, the substance is a fixed gas so cannot be liquefied by increasing the pressure

• The relationship approximates to Boyle’s law

Nitrous oxide isotherms 36.4°C

• Critical temperature line

• Demonstrates a sharp inflexion at 73 bar (critical pressure) where liquefaction occurs

• At critical temperature, any vapour is on a temperature and pressure ‘knife-edge’; any tiny change causes either liquefaction or transformation to a fixed gas so very little vapour exists

• Sharp pressure rise with further volume decrease as liquids are incompressible

• Remember, liquefaction cannot occur above a substance's critical temperature

Nitrous oxide isotherms 20°C

• Room temperature line

• So far beneath critical temperature, vapour will not transform to the gas

• Steady linear increase as vapour is compressed

• Plateau in pressure as further volume reduction now results in liquefaction

• Vapour/liquid mixes exist over a wide volume range

• Sharp rise once all the vapour is liquefied

Nitrous Oxide Cylinders

• Stored as a liquid where the vapour pressure is 44 bar.

• Liquid is less compressible than vapour so cylinders have a filling ratio of 0.75 as to allow expansion and prevent explosion (warmer climates 0.67).

• The filling ratio describes the weight of fluid within a nitrous cylinder compared with the weight of the cylinder when filled completely with water

  • based on weight not volume; differing densities of N₂O (1222 kg/m³) and water (1000 kg/m³) so 0.75 filling ratio does not give a cylinder 75% full by volume

• Stored vertically.

• Tare weight is the weight of the empty cylinder.

• During continuous use of nitrous oxide cylinders, latent heat of vaporisation causes cooling, leading to a gradual fall in pressure rather than a constant pressure until the liquid is exhausted.