Cambridge A Level Physics 9702 — 2018 Oct/Nov Paper 5 · Variant 2

1 A student is investigating how the rate at which water evaporates varies with temperature. It is suggested that the relationship between the volume of water evaporated per unit time Y and the Celsius temperature θ of the water is Y = kθ s where k and s are constants. Design a laboratory experiment to test the relationship between Y and θ. Explain how your results could be used to determine values for k and s. 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 temperature (of the water)/θ is the independent variable and volume per unit time/Y is the dependent variable or vary θ and determine Y 1 keep temperature of room/surroundings constant 1 Methods of data collection labelled diagram of workable experiment including: • beaker open to air • water, labelled • workable method to heat water 1 method to determine (change in) volume, e.g. measuring cylinder or method to determine (change in) mass, e.g. top-pan balance 1 measure time with a stop-watch/timer (for change in volume/mass or evaporation) 1 use a thermometer to measure θ or labelled thermometer in water in diagram 1 Method of analysis plot a graph of lg Y against lg θ (or ln Y against ln θ) 1 s = gradient 1 k = 10y-intercept (for ln Y against ln θ: k = ey-intercept) 1 Question Answer Marks Additional detail including safety considerations Max. 6 D1 use of (protective) gloves to handle hot beaker/water D2 keep surface area constant (by using the same cylindrical container) D3 keep water temperature constant (while water is evaporating) D4 method to keep temperature constant while water is evaporating e.g. adjust heater/gently heat water to maintain temperature/use a water bath D5 use a large surface area to increase the rate of evaporation D6 initial volume final volume V or time time Y − ∆ = D7 lg lg lg Y s k θ = + D8 relationship valid if a straight line D9 insulation/lagging around (sides) of beaker (not a lid) D10 switch off fans or close windows to avoid draughts

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2 A student is investigating the current in a circuit. The circuit is set up as shown in Fig. 2.1. E r A P Q Fig. 2.1 Resistors, each of resistance R, are connected in parallel between P and Q. The current I is measured. The experiment is repeated for different numbers n of resistors between P and Q. It is suggested that I and n are related by the equation R E = I + r c n m where E is the electromotive force (e.m.f.) and r is the internal resistance of the power supply. 1 1 (a) A graph is plotted of on the y-axis against on the x-axis. I n Determine expressions for the gradient and the y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] 1(b) Values of n, I and are given in Fig. 2.2. n 1 1 / A–1 n I / mA n I 2 34 ± 2 0.50 3 46 ± 2 0.33 4 56 ± 2 0.25 5 66 ± 2 0.20 6 76 ± 2 0.17 7 84 ± 2 0.14 Fig. 2.2 1 Calculate and record values of / A–1 in Fig. 2.2. I 1 Include the absolute uncertainties in I. [2] 1 1(c) (i) Plot a graph of / A–1 against n. I 1 Include error bars for I. [2] (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) gradient = R E y-intercept = r E 1 2(b) 29 or 29.4 22 or 21.7 18 or 17.9 15 or 15.2 13 or 13.2 12 or 11.9 1 absolute uncertainties in 1 / I from ±2 (or ±1) to ±0.2, ±0.3 or ±0.4. Allow a mixture of significant figures. 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 / I plotted correctly. All error bars to be plotted. 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 left of (0.50, 29.6) and line should pass between (0.210, 16) and (0.225, 16). 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 2(d)(i) E calculated using gradient. Correct substitution of numbers required. 470 470 gradient E = = (c)(iii) 1 r calculated using y-intercept. Correct substitution of numbers required. -intercept r E y = × 1 E and r determined using correct method with: • Unit of E with correct power of ten – e.g. V, A Ω • Unit of r with correct power of ten – e.g. Ω, V A–1 • E and r given to 2 or 3 significant figures. 1 Question Answer Marks 2(d)(ii) Percentage uncertainty in r determined. Correct substitution of numbers required. %uncertainty in gradient + %uncertainty in R (1.06%) + %uncertainty in y-intercept or %uncertainty in E + %uncertainty in y-intercept Maximum/minimum methods: max max -intercept max r y E = × ( ) max 475 max max -intercept mingradient R r y = × min min -intercept min r y E = × ( ) min 465 min min -intercept max gradient R r y = × 1

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