# Chapter 4b – Physics Answers

## Abstract

### Question 1: FTFFT

SI stands for Système Internationale (d’Unités). There are seven base units (from which all other units can be derived).

A neat way of remembering this mnemonic is ‘SM2ACK2’:

• Second (s)

• Metre (m)

• Mole (mol)

• Ampère (A)

• Candela (cd) – a measure of luminous intensity

• Kilogram (kg)

• Kelvin (K) (note – not degrees)

They make up the fundamental buildings blocks of all other units of measurement. For example, the unit of frequency is the hertz; but hertz it is not a base unit. It is a derived unit and is defined as 1 s–1. Another example is that of force. Statement e gives the correct derivation of the newton. Other derived units include pressure, power, volume, electrical potential, energy, charge and resistance. This list is not exhaustive.

### Question 2: FTFFT

Beware of subtle changes in the wording. There are some trick questions here, testing your knowledge. The mole is the number of atoms of carbon-12, not 14 in 12 g (0.012 kg). The metre was previously defined as the distance occupied by 1 650 763.73 wavelengths of the standard radiation of krypton-86, but now this subdivision of the speed of light is used (since 1983). Statement c gives the definition of a joule. 1 watt is 1 joule per second (N.m.s−2). The definition of 1 pascal is the pressure of 1 newton per square metre.

### Question 3: TFTTF This simple MCQ is a primary exam favourite. It tests understanding of the many different units of pressure measurement. Unfortunately, in clinical practice we still haven’t got round to standardizing our different gauges.

### Question 4: TTFFF

This question is worded to ensure candidates truly understand the concept of the kelvin. The first two statements are the correct definitions. The triple point occurs at 273.16 K which is 0.01 °C ; °C is a derived unit. The freezing point of water, which is 0 °C, is 273.15 K.

Heat capacity is the amount of heat (a form of energy, measured in J) required to raise the temperature of an object by 1 K, so its unit would be J.K–1. (Specific heat capacity is the amount of energy required to raise the temperature of 1 kg of a specific object by 1 K.)

### Question 5: TFFTT

There are many techniques used for measurement of temperature. These are indeed four of them. The bimetallic strip is arranged in a coil, and as temperature changes, the degree of uncoiling is shown by a pointer. The description in statement b is the basis for the thermocouple. In a platinum resistance wire, resistance increases proportionally with temperature, not exponentially. The thermistor is a small semiconductor bead and resistance does decrease exponentially. The Seebeck effect is described in statement b.

### Question 6: FFTFF

Body temperature is regulated to around 37 °C. The standard deviation is about 0.2 °C, although there is variability throughout the day of up to 0.7 °C. Brown fat thermogenesis is a feature of the neonate, not the child. The specific percentages of heat loss from different modalities are variable. However, anaesthetists should know which modalities are more problematic. Roughly speaking, radiation does account for about 40–50% of heat loss, respiration (along with evaporation from the skin) accounts for about 20% of the loss, and convection can account for up to 30–40% of heat loss. Conduction is relatively insignificant in air, but increases markedly in water.

### Question 7: TTFTF

Latent heat is the energy required to change the state of a substance without changing its temperature. Somewhat confusingly, the reaction can be in either direction (liquid to vapour or vapour to liquid) so statement a is true. Latent heat falls as temperature rises and is zero at the critical temperature, as no further heat is required to convert the liquid to a gas, as it cannot exist in the liquid phase at that temperature. Nitrous oxide cylinders contain liquid nitrous oxide with vapour above. As nitrous oxide vapour is removed from a cylinder, heat will be required to vaporize more of the remaining liquid nitrous oxide. This is taken from the surrounding fluid and cylinder walls, making them cold (adiabatic cooling). Water vapour in the surrounding air may condense or even freeze on the cold walls of the cylinder. The drop in temperature of the remaining liquid will reduce the resultant vapour pressure (as the saturated vapour pressure is also related to temperature) and so the gauge will under-read until the cylinder is switched off and thermal equilibrium is restored. The critical temperature of nitrous oxide is +36.5 oC. This means it is inhaled as a vapour (below its critical temperature) but exhaled as a gas (above its critical temperature), a popular viva question!

### Question 8: FTTTT

Boyle’s law states that volume is inversely proportional to absolute pressure, not gauge pressure. Statement c gives the third gas law, Gay-Lussac’s law. However, Gay-Lussac has been attributed to both the second (Charles’) and third laws. Strictly speaking, the third law was first described by Amontons 100 years before Gay-Lussac. Standard temperature and pressure (STP) are described as 273.15 K (note not ‘degrees’ K) and 101.325 kPa. These equate to 0 oC and 760 mmHg, but the correct SI units should ideally be used.

### Question 9: TFTTT

The molecules of an ideal gas must be identical and not interact with each other (so no forces exist between them). However, there is no true ideal gas in existence. All molecules are subject to the Newtonian laws of mechanics. Nitrogen, oxygen, hydrogen, noble gases and carbon dioxide are generally regarded to behave like ideal gases within accepted tolerances. The movement of molecules within an ideal gas is at random.

### Question 10: TFTTT

Statement a is Avogadro’s hypothesis. Statement b should be 6.022 × 1023. The critical temperature is the highest temperature at which a gas can still be liquefied by pressure alone. This is the critical pressure. Questions originating from definitions of critical temperature and pressure are common. At the critical temperature, a gas can be in a gaseous form or a vapour. Above this temperature, it can only exist as a gas.

### Question 11: TTFTT

Regression analysis determines the magnitude of change of one variable produced by the other variable. It requires the formulation of a mathematical model to explain the data and results in an equation in the form

y = mx + c

y being the dependent variable, x the independent variable, m being the gradient of the line demonstrating the regression coefficient, and c being the intercept which defines the position of the line. Whilst the correlation coefficient is an indicator of the ‘goodness of fit’ this is yielded from correlation analysis, not linear regression analysis. It utilizes the least squares method to find the regression line that has the most explanatory power and least error. Although the data do not need to be normally distributed to perform linear regression analysis, both variables must be continuous data.

### Question 12: FTFTF

Randomization refers only to the method of selecting individuals to each of the study groups. It is an important way to reduce selection bias. There are a number of ways in which randomization can be performed, including using random number tables, a random number generator or by simply tossing a coin. Using randomization, any individual in a population has the same chance of being allocated to each treatment group as any other individual in the sample population.

### Question 13: TFTFT

In normally distributed data, the mean, median and mode are the same. In skewed data this is not the case. If the data are positively skewed, the peak (or the mode) lies to the left, with the tail sloping off to the right towards the more positive values (Figure 4.13.1). The mean lies towards the tail of the curve and the median value sits between the mode and the mean. This type of data can sometimes be normalized by logarithmic transformation of the data.

The graph below demonstrates the positive skew of the data mentioned in the question. Median survival gives a better indication of length of life after diagnosis than the mean does. The median is the middle value of a data series and thus if the median survival was three years then 50% of the population (300 patients) would be deceased at three years. Because the data are positively skewed the majority of the population lies to the left. Figure 4.13.1 Skewed data: mode, median and mean.

### Question 14: TTFFT

A Type 1 error is also known as an α error or a false positive (rejection of the null hypothesis). The P value represents the probability that a Type 1 error will be made. Type II (β or false negative) errors are reduced by increasing the sample size, not Type I errors. Blinding will not affect the likelihood of there being a difference between groups.

### Question 15: TFTTT

Type II (β) errors are false negatives and would lead to an incorrect acceptance of the null hypothesis. Power is 1 – (the Type 2 error rate).

### Question 16: TFTFF

Statement a is one of the definitions of a normal (or Gaussian) distribution. The mean (the average of all the values), the median (the value with 50% of the data points on each side of it) and the mode (the most frequently occurring value) are all the same. ‘Normality’ is usually quoted as the 95% confidence interval and this would be represented by the mean ± 1.96 standard deviations. Student’s (unpaired) t-test is the classic way to compare two normally distributed sets of data. Normally distributed continuous data are parametric, but they can be analyzed using non-parametric tests. The converse is not true, however.

### Question 17: TFTFT

Mann–Whitney is a non-parametric test for ordinal data. Chi-squared is used for nominal data. Accurately measured but non-normally distributed data are non-parametric. These tests need not be more complicated.

### Question 18: TTFFF

Statements a and b essentially describe the chi-squared test. Continuous variables would use the t-test family. It cannot be less than zero.

### Question 19: TFTFF

Categorical (or nominal or attributive) data are those where items are grouped according to their attributes into categories – hair colour, for example. There is no ranking and no continuity between groups. Ordinal data need to be managed carefully as they have numerical associations, but are not continuous (e.g. ASA; you can’t be ASA grade 2.5!)

### Question 20: FFFTT

The forest plot is used in documenting meta-analyses. Individual trials are shown as a square with an area proportional to the weight given to that trial in the meta-analysis. From each side of the square extends a line that represents the confidence interval. The combination of all the trials is represented as a diamond.

### Question 21: TFTTF

Statement a is the basic negative exponential definition. Alcohol observes zero-order kinetics (a fixed amount is removed per unit time, regardless of the initial amount present). The Manley is a time-cycled pressure-generating ventilator. This is regarded as a physiological build-up negative exponential because the rate of increase in y is decreasing exponentially with time. In a PA catheter, the decay in concentration of indicator (temperature) is governed by an exponential process. Using TCI for propofol involves a three-compartment model of concentration and so does not demonstrate a true exponential decay.

### Question 22: TTTTF

At its most basic definition, the joule is the work done when a force of 1 newton is applied over 1 metre (1 Nm). As a newton is the force required to accelerate a mass of 1 kg by 1 m.s−2, a joule is also 1 kg.m2.s−2; 1 dyne is the force required to accelerate 1 g by 1 cm. s−2 and so 100 000 dyne is equivalent to 1 N; 1 pascal (Pa) is 1 N.m−2, which makes statement d true as well. Statements e and b cannot both be correct. This is a simple case of learning the units.

### Question 23: TTFFF

Laminar flow is governed by the Hagen–Poiseuille equation:

Q = πPr4/8ηl

where Q = flow, P = pressure, r = radius of tube, η = viscosity, l = length of tube.

Reynolds number gives a likelihood of flow being turbulent. This is defined as

NR = vρd/η

where v = velocity of flow, ρ = density of fluid, d = diameter of the tube, η = viscosity of fluid.

If this number is greater than 2000, flow is likely to be turbulent, but not guaranteed, especially if local changes in the tube cause variability in flow. In turbulent conditions, flow is inversely proportional to the square root of the density.

### Question 24: TTFFT

In the oscillatory flowmeter, the flow is directed in alternating directions by the Coanda effect. This oscillation is proportional to the velocity of the fluid. In the pneumotachograph, flow across a gauze screen in the stream causes a drop in pressure. Pressure is measured on either side of the screen and the difference is related to the velocity of flow. In the rotameter the bobbin is supported by the gas flow; as the upward pressure balances the downward force of gravity on the bobbin, pressure must be constant. The orifice (around the bobbin) is variable. The Wright respirometer measures volume, not flow. As there is a degree of drag in the gearing inside the device, low volumes may not be accurately measured.

Table 4.24.1

Equipment that measures flow Equipment that measures volume
Rotameter Benedict Roth spirometer
Pneumotachograph Vitalograph
Wright’s peak-flow meter Wright’s respirometer
Mass flowmeter Dry gas meter

### Question 25: TTTFF

Statements a–c are the correct definitions. The definition of osmolality is correct, but Murphy did not describe it. His law states that ‘if anything can go wrong, it will!’ Beer’s law states that the absorption by a given thickness of solution of a given concentration is the same as that of twice the thickness of solution of half the concentration. Lambert’s law states that each layer of equal thickness absorbs an equal fraction of the radiation passing through.

### Question 26: TFFFF

The lower the impedance, the more current will flow in the event of touching a live connection. It needs therefore to be low enough to allow dissipation of electrostatic charges but high enough to protect against electric shock. British Standard EN60601 gives requirements for medical electrical equipment, not footwear. Water will reduce impedance.

### Question 27: TTFFT

Class I equipment has no symbol. There must at least be a fuse in both the live and neutral circuits. In the UK, the plug also has a fuse in it. Double insulated equipment is Class II. Class I is the least safe. The floating circuit is the safest for use in theatres. Any part of the equipment (especially the casing, if conducting) should be earthed for protection in the event of a short circuit.

### Question 28: TTTFT

Double-insulated equipment is known as Class II equipment. The symbol is as given. As there are two layers of protection between the user and any live parts, an earth wire is not required. Class III equipment must run on a supply of no more than 24 V. The likely current flow caused by a short circuit in a system using 240 V mains supply with only skin impedance (about 10 kΩ) is 24 mA. Reinforced insulation is an acceptable alternative to double insulation.

### Question 29: FTTFT

Severity increases with decreasing frequency. Mains frequency (50 Hz) is already quite low and so its lethality is high. It is used at this frequency because of its transfer efficiency. Diathermy by contrast is at much higher frequency (0.5–1 MHz or higher). At this frequency, the penetration of the current is low and so lethality is lower. The severity of microshock increases as the frequency of the current decreases, so the risk is greatest at low frequencies, such as mains frequency and with direct current. It is possible for normally functioning equipment to induce currents in, for example, pacing leads and cause microshock. An oesophageal temperature probe may, rarely, cause microshock.

### Question 30: FFTTF

No type C equipment is described. Type CF equipment may be connected to the heart. The square box and stick man symbol is for type BF equipment. Type B has no box. The maximum for Class I type B equipment is 500 µA. It is 100 µA for Class II type B. All these standards relate to single faults. Type CF equipment has standards of 50 µA for Class I and 10 µA for Class II.

### Question 31: FTTTT

The Penaz technique (also known as finapres) gives a continuous measurement of blood pressure. It is a non-invasive technique using an infrared photoplethysmograph (like the ‘sats probe’) to measure pulse volume and a servo-controlled cuff around the finger (like a small non-invasive blood pressure cuff) to vary pressure to keep the volume constant. The pressure applied is related to arterial pressure. The flow is not interrupted (although it is restricted) during this technique and so it can be used for continuous monitoring.

### Question 32: FFTFT

Small syringes can develop very high pressures and cause damage either to arterial walls or the pressure transducer. The recommended smallest size for flushing is 5 ml. Continuous flush should be at no more than 4 ml.h–1. The ideal cannula is short, with parallel sides and coated with a non-stick material like Teflon®. Good asepsis is required, but full surgical precautions are not currently mandated. Any artery can be used, but ideally one with collateral cover from another should be used so that a clot in the cannulated artery does not cause distal ischaemia. Either the radial artery in the wrist or the dorsalis pedis artery in the foot are the most common sites, but the ulnar and posterior tibial are also options. It is recommended to avoid brachial, femoral and similar arteries if possible.

### Question 33: TTTTT

Fibreoptic transducers are available, but are expensive and not routinely used. They are useful, for example, in MRI scanners, as they are not affected by the magnetic field. The original oscillotonometer used two cuffs. Modern non-invasive methods use the same cuff for occlusion and sensing. Accurate blood pressure readings rely on a constant volume pulse. In dysrhythmias, there can be a wide beat-to-beat variation, which will cause inaccuracies. Radial artery compression techniques are available, but not widely used in clinical situations. Ultrasound Doppler can measure frequency changes and calculate pressure. Many of these techniques are prone to user intervariability and calibration problems.

### Question 34: TFTTT

Mercury manometers can theoretically measure any pressure, but are limited by the practicalities of size. As atmospheric pressure is 760 mmHg, a 760 mm column of mercury will be required. Any higher pressures than this become unwieldy. To measure gauge pressure, the top must be open (usually sealed with an air-permeable membrane to prevent leakage of mercury). A sealed manometer with a vacuum above the mercury will measure absolute pressure. A standard manometer will measure gauge pressure. The tube can be sloped, but the measurement must be taken in a vertical plane (or the scale adapted to reflect this). Surface tension will affect the result. Water manometers will over-read and mercury ones will under-read due to this effect. This effect is reduced by using a wide-bore tube.

### Question 35: FTFTF

Aneroid gauges do not use liquid; the name comes from the Greek for ‘not wet’ or ‘without liquid’. Sealed aneroid gauges measure absolute pressure. One with an open interior measures gauge (or differential) pressure. They are ideal for measuring high pressures.

### Question 36: TTFTF

Anything that reduces the transmission of the pressure along the system will cause damping. Blood clots may completely occlude the system. Air bubbles will affect the resonant frequency and increase damping. A long cannula will not affect damping directly, but increases the risk of blood clots. Anything that interrupts flow may affect damping; three-way taps are an example of this. A stiff cannula will reduce damping, not increase it.

### Question 37: TTFFT

Damping reduces the amplitude of oscillation. Mean pressure will therefore be unaffected, but as systolic and diastolic pressures represent the maximum and minimum amplitude, these will tend toward the mean as damping increases. Heart rate (as the frequency of oscillation) is unaffected. Stroke volume is calculated from the amplitude and so will be affected by damping.

### Question 38: FFFTF

It is not ideal to cannulate the brachial artery, as a clot in this vessel will cause forearm ischaemia. This does not mean this artery must not be used. The transducer should be kept at the level of the heart, not the level of the limb. Normal saline is used in the arterial line, but the risk of microshock is increased by using saline, as it conducts electricity. Standard transducers have a resonant frequency of about 100 Hz but it is only as the frequency falls below 40 Hz that significant resonance is seen. Strain gauges are relatively insensitive to temperature variation.

### Question 39: FFFFF

Any cuff can cause nerve damage, either directly or by interrupting the blood supply to the nerve, but it is not as high as 1 in 100. Atrial fibrillation will cause significant inaccuracy in the measurements made. This is a contentious point, but most texts claim that the systolic pressure is the most accurate measurement (the first presence of oscillation). Mean is next most accurate (maximum amplitude of oscillation). While the original oscillotonometer required two cuffs (one to occlude, one to sense), modern devices use the same cuff for both.

### Question 40: TFFFT

Statement a is a definition of optimal damping. This usually occurs with a coefficient of 0.6–0.7. Underdamping does lead to resonance, but the signal will overshoot, not undershoot. Underdamping might allow resonance, but this does not give better reproduction of the intended waveform. Optimal damping allows a rapid response (at the expense of a small amount of overshoot). Critical damping (a coefficient of 1.0) will lead to no overshoot, but a slow response.

### Question 41: FFTFT

Adequate return of neuromuscular function may be derived clinically. Signs include sustained head lift for at least 5 seconds, generating a VC of at least 10 ml.kg–1 or generation of an inspiratory pressure of at least –25 cmH2O. Tidal volume is not a reliable guide to recovery, as normal volumes can be generated with only 20% functional diaphragm muscle receptor activity. In addition, oxygen saturations can be maintained with minimal ventilatory effort. The carbon dioxide levels will increase, however.

### Question 42: FFTFT

PiCCO is based on the principle of pulse contour analysis. PiCCO stands for Pulse Induced Contour Cardiac Output. PiCCO requires a standard central line with a thermistor on the distal lumen and a special arterial cannula with a thermodilution sensor. The arterial cannula is sited in the femoral, brachial or axillary artery.

### Question 43: TFTFF

In TOF, the ratio of the fourth to the first twitch is measured. Four twitches of 2 Hz each are applied over 2 seconds. One should leave a gap of 10 seconds between each TOF. As the muscle relaxant is administered, fade is noticed first, followed by the disappearance of the third then the second and finally by the first twitch. On recovery, the first twitch is the first to appear, then the second, followed by the third and fourth; reversal of the neuromuscular block is easier if the second twitch is visible. For upper abdominal surgery, at least three twitches must be absent to achieve adequate surgical conditions.

### Question 44: FFFFF

In order to reliably detect muscular twitches as neuromuscular blocking drugs are being cleared from the junction, a nerve stimulator must be able to deliver a current that is greater than the current required to produce a maximal twitch. This is known as a supramaximal twitch current. In general, with well-applied electrodes, the maximum twitch current is around 60 mA (not microamps, as in the question) so a reliable stimulator must produce more than this. Most sources recommend about 80 mA.

Mains power might, in the event of a fault, be transmitted directly to the patient through the highly conductive electrodes. This could be life-threatening so stimulators are battery powered. It is also far more convenient for batteries to be used, as the stimulator is often moved or used in locations where mains power would be inconvenient. There are some exceptions to this. Some anaesthesia workstations have neuromuscular monitoring modules that are mains powered. The danger of mains conduction is ameliorated using optoisolators to ensure that no conductive path is available between the mains power and the patient.

If the block has fully developed then there will be no twitch at any current. This is the basis of the monitoring. The supramaximal twitch must be tested before the block is initiated.

The leads are generally coloured red and black for positive and negative, respectively. This allows identification of the leads so that the negative can be placed distally, which minimizes current required.

Most neuromuscular blocker monitors supply twitches of 0.2 s. It is not normal practice to use variable-width twitches and this function is not supplied in stimulators for this purpose. They often offer single twitches, trains of four (four twitches delivered in 2 s) and tetanic sequences for measuring different types of block and for use with different agents.

### Question 45: FTTTF

Cardiac output monitors can be classified as non-invasive, invasive, and semi-invasive or minimally invasive. Transthoracic impedance is a non-invasive technique. Other non-invasive techniques include radionuclide scans, magnetic resonance imaging and transthoracic Doppler.

Transthoracic impedance applies a high-frequency, low-magnitude current, which is detected using six externally placed electrodes. Thoracic impedance is indirectly proportional to changes in blood volume, reflecting changes in the cardiac cycle.

This technique has a number of disadvantages, including its inaccuracy in the presence of arrhythmias.

### Question 46: FFTTF

In laminar flow, fluid moves in a steady manner, flow rate is greatest at the centre of the flow stream (twice the average flow rate), a pressure difference must exist for fluid to flow, flow is directly proportional to this pressure difference and resistance of the tube is calculated by the ratio of pressure to flow. A number of variables must be known to quantify the relationship between pressure and flow. Both the Hagen–Pouseille equation and Reynolds’ estimation are important.

### Question 47: FTTFF

In turbulent flow, flow is characterized by swirls and eddies; the transition of laminar to turbulent flow can occur at constrictions. Fluid velocity varies across the cross-sectional area of the tube. Flow is proportional to the square root of pressure, resistance is no longer constant (the relationship between pressure and flow is no longer linear), density of the fluid is the important determinant in turbulent flow.

### Question 48: FFFFT

Wright’s respirometer is a compact and light respirometer used to measure tidal volume and minute volume. For clinical use, the respirometer reads accurately (±5–10%) within the range of 4–24 l.min–1. A minimum flow of 2 l.min–1 is required for the respirometer to function accurately. A paediatric version exists with a capability of accurate tidal volume measurements of between 15 and 200 ml.

### Question 49: FFFTF

The pneumotachograph measures gas flow, sensing the change in pressure across a fixed resistance through which gas flow is laminar. Density and viscosity of the gas can alter the accuracy; compensation is by continuous gas composition analysis via a sampling tube.

### Question 50: FTTFT

Oct 24, 2020 | Posted by in ANESTHESIA | Comments Off on Chapter 4b – Physics Answers
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