Cambridge A Level Physics 9702 — 2018 Oct/Nov Paper 5 · Variant 3

1 A student is investigating how the boiling point of a salt solution varies with pressure. It is suggested that the relationship between the Celsius temperature θ at which the water of the solution starts to boil and the air pressure P is θ = kσP q where σ is the density of the solution and k and q are constants. Design a laboratory experiment to test the relationship between θ and P. Explain how your results could be used to determine values for k and q. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed, • the measurements to be taken, • the control of variables, • the analysis of the data, • any safety precautions to be taken. 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Mark scheme: 1 Defining the problem P is the independent variable and θ is the dependent variable, or vary P and measure θ. (Allow θ is the independent variable and P is the dependent variable.) 1 keep density of salt solution constant or keep σ constant 1 Methods of data collection labelled diagram of workable experiment including: • sealed container e.g. bell jar, sealed conical flask • tube connected to pump (for changing pressure) or other workable method • salt solution, labelled 1 workable method to heat salt solution within the sealed container, e.g. hot plate/(electrical) heater 1 description of pressure gauge or manometer to measure P 1 use of a thermometer to measure θ or labelled thermometer (in salt solution) in diagram 1 Method of analysis plot a graph of lg θ against lg P (or ln θ against ln P) 1 q = gradient 1 k = 10y-intercept / σ (for ln θ against ln P: k = ey-intercept / σ) 1 Question Answer Marks Additional detail including safety considerations Max. 6 D1 safety precaution relating to pressure, e.g. safety screen D2 use of (protective) gloves to handle hot salt solution/beaker/flask D3 density of salt solution or ρ given by m / V D4 measuring cylinder to measure volume and difference in top pan balance/scales readings to measure mass of salt solution D5 slowly/gradually increase/decrease the temperature/pressure D6 measure P and θ when salt solution starts to boil D7 lg lg lg q P k θ σ = + D8 relationship valid if a straight line D9 identification of when (salt solution) starts to boil, e.g. wait until (vapour) bubbles are on the surface or surface moves or temperature remains constant (for heating methods) D10 recheck that density of salt solution is constant/add water to keep density constant/take multiple solutions from a large volume

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2 A student is investigating the electric potential near a charged metal sphere. The sphere is suspended from the ceiling as shown in Fig. 2.1. ceiling insulated thread charged sphere L position of flame probe Fig. 2.1 A flame probe is used to measure the potential V at a distance L from the surface of the sphere. The experiment is repeated for different distances from the sphere. It is suggested that V and L are related by the equation Q V = 4πε0(L + a) where Q is the charge on the sphere, a is the radius of the sphere and ε0 is the permittivity of free space. 1 (a) A graph is plotted of on the y-axis against L on the x-axis. V Determine expressions for the gradient and the y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of L and V are given in Fig. 2.2. 1 L / m V / kV / 10–3 V–1 V 0.018 1.25 ± 0.05 0.036 1.05 ± 0.05 0.053 0.90 ± 0.03 0.068 0.80 ± 0.03 0.089 0.70 ± 0.02 0.113 0.60 ± 0.02 Fig. 2.2 1 Calculate and record values of / 10–3 V–1 in Fig. 2.2. V 1 Include the absolute uncertainties in . [2] V 1(c) (i) Plot a graph of / 10–3 V–1 against L / m. V 1 Include error bars for . [2] V (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = .......................................................... [2]

Mark scheme: 2(a) y-intercept = 4πε0a / Q 1 2(b) 0.800 or 0.8000 0.952 or 0.9524 1.1 or 1.11 1.3 or 1.25 1.4 or 1.43 1.7 or 1.67 1 absolute uncertainties in 1 V : ±0.03 to ±0.05 or ±0.06 1 2(c)(i) Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square. 1 Error bars in 1 V plotted correctly. All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Line of best fit drawn. Points must be balanced. Line should pass to the right of (0.019, 0.800) and line should pass between (0.104, 1.6) and (0.108, 1.6). 1 Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted. 1 Question Answer Marks 2(c)(iii) Gradient determined with clear substitution of points from line of best fit into ∆y / ∆x. Distance between points must be at least half the length of the drawn line. 1 uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(c)(iv) y-intercept determined by substitution into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution into y = mx + c. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) Do not allow if false origin used. 1 Question Answer Marks 2(d)(i) Q calculated using gradient. Correct substitution of numbers required. 10 10 1.11 10 1.11 10 gradient (c)(iii) Q − − × × = = 1 a calculated using y-intercept. Correct substitution of numbers required. 10 -intercept 1.11 10 Q y a − × = × or -intercept gradient y a = 1 Q and a determined using correct method with: • Unit of Q with correct power of ten – C, F V • Correct power of ten for a • Q and a given to 2 or 3 significant figures. 1 Question Answer Marks 2(d)(ii) Percentage uncertainty in a determined. Correct substitution of numbers required. %uncertainty in Q + %uncertainty in y-intercept or %uncertainty in gradient + %uncertainty in y-intercept Maximum/minimum methods: 10 max -intercept max max 1.11 10 y Q a − × = × max -intercept max mingradient y a = 10 min -intercept min min 1.11 10 y Q a − × = × min -intercept min max gradient y a = 1

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