A-LevelPhysicsThermodynamics9702/31 · May/June 2021 · Q220 Marks

In this experiment, you will investigate how the rate of cooling of a hot liquid depends on its volume.

(a)You have been provided with a cup. The diameter of the base of the cup is d, as shown in Fig. 2.1. Measure and record d. d = ..................................................... [1][1]
(b)• Pour boiling water into the cup until it is approximately one-third full. • When the temperature of the water is 75°C, start the stop-watch. Record this starting temperature θ₀. θ₀ = ..................................................... °C • After two minutes, measure and record the temperature θ. θ = ..................................................... °C • Calculate Δθ using Δθ = (θ₀ – θ). Δθ = ..................................................... °C [1][1]
(c)(i)The height of the water in the cup is h and the diameter of the surface of the water is D, as shown in Fig. 2.2. Measure and record h and D. h = ..................................................... D = ..................................................... [2][2]
(c)(ii)Estimate the percentage uncertainty in your value of h. Show your working. percentage uncertainty = ..................................................... [1][1]
(c)(iii)Calculate C where C = (D³ - d³) / (D - d) C = ..................................................... [1][1]
(c)(iv)Justify the number of significant figures that you have given for your value of C. [1][1]
(d)• Empty the cup. • Repeat (b), (c)(i) and (c)(iii) with the cup approximately two-thirds full. θ₀ = ..................................................... °C θ = ..................................................... °C Δθ = ..................................................... °C h = ..................................................... D = ..................................................... C = ..................................................... [3][3]
(e)(i)It is suggested that the relationship between Δθ, h and C is Δθ = k / √(hC) where k is a constant. Using your data, calculate two values of k. first value of k = ........................................................................................... second value of k = ........................................................................................ [1][1]
(e)(ii)Explain whether your results support the suggested relationship. [1][1]
(f)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment. 1. 2. 3. 4. [4][4]
(f)(ii)Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures. 1. 2. 3. 4. [4][4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[1] 2(a) Value of d to the nearest mm with unit.
[1] 2(b) Correct calculation of temperature change Δθ.
[1] 2(c)(i) Value of h with unit.
[1] D > d.
[1] 2(c)(ii) Percentage uncertainty based on absolute uncertainty Δh in the range 2–6 mm. If repeat readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty.
[1] 2(c)(iii) Correct calculation of C.
[1] 2(c)(iv) Justification for significant figures in C linked to s.f. in D and d or linked to s.f. in (D – d).
[1] 2(d) Second values of θ₀ and θ.
[1] Second values of h and D.
[1] Temperature decreases in both experiments and second value of Δθ < first value of Δθ.
[1] 2(e)(i) Two values of k calculated correctly. The final k values must not be written as fractions.
[1] 2(e)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated by the candidate.
[4] 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure h with reason, e.g. scale of ruler does not start at the end/opaque cup/water too hot/rule in water changes water level. C Difficult to measure D with reason, e.g. parallax. D Large % uncertainty (error) in Δθ or thermometer is not precise enough to measure a small change in temperature. E Difficulty with taking temperature at the end of the two-minute period with reason, e.g. cannot look at stop-watch and thermometer simultaneously. 1 mark for each point up to a maximum of 4.
[4] 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Use a transparent cup/ruler without a space at end/measure (empty depth – depth to water surface) with detailed description e.g. use rod at right angles to a rule across top of cup to reach water surface or cup bottom. C To measure D or inside of cup, use calipers/dividers/vertical pointers/travelling microscope. D Improved method to measure Δθ e.g. more precise thermometer/thermometer reading to 0.1 °C/thinner capillary in thermometer/more sensitive thermometer or allow experiment to go on for more than two minutes. E Method for simultaneous measurement of temperature and time e.g. sound to mark two-minute period/temperature probe linked to data logger system/video with thermometer and timer in view. 1 mark for each point up to a maximum of 4.