9702 Physics March 2025 Question paper 52

2 A student investigates the cooling of a liquid in a beaker.

The temperature θR of the laboratory is measured using a thermometer.

Hot water is added to an insulated beaker, as shown in Fig. 2.1. stand thermometer beaker bench insulation heat-proof mat water Fig. 2.1

The thermometer measures the temperature of the water. At time t the temperature of the water is θ.

A series of readings of t and θ are taken.

It is suggested that θ and t are related by the equation θ = θR + (θ0 – θR) e–( t K)

where θ0 is the temperature at t = 0 and K is a constant.

(a) A graph is plotted of ln (θ – θR) on the y‑axis against t on the x‑axis.

Determine expressions for the gradient and y‑intercept.

gradient = y‑intercept = [1] , , ` (b) Values of t and θ are given in Table 2.1. Table 2.1 t / min θ / °C (θ – θR) / °C ln ((θ – θR) / °C) 6.0 75.0 ± 0.5 12.0 64.5 ± 0.5 18.0 57.0 ± 0.5 24.0 50.0 ± 0.5 30.0 44.5 ± 0.5 36.0 41.0 ± 0.5

The value of θR is (18.5 ± 0.5) °C.

Calculate and record values of (θ – θR) / °C and ln ((θ – θR) / °C) in Table 2.1.

Include the absolute uncertainties in (θ – θR) and ln ((θ – θR) / °C). [2]

(c) (i) Plot a graph of ln ((θ – θR) / °C) against t / min. Include error bars for ln ((θ – θR) / °C). [2]

(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2]

(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

gradient = [2] , , ln (( – R) / °C) θ θ 4.1 4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 t / min , ,

(iv) Determine the y‑intercept of the line of best fit. Include the absolute uncertainty in your answer.

y‑intercept = [2]

(d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of K and θ0. Include appropriate units.

K = θ0 = [2]

(ii) Determine the absolute uncertainty in your value of θ0.

absolute uncertainty = [1]

(e) Determine the time t for the temperature to reach 25.0 °C.

t = min [1] [Total: 15] , ,

1 Fig. 1.1 shows two identical cylindrical metal conductors P and Q, each of length L and cross‑sectional area A. L X Q P q p Fig. 1.1

The conductors are placed parallel to each other. The perpendicular distance from the midpoint of P to point X is p. The perpendicular distance from the midpoint of Q to point X is q.

The two conductors are electrically connected in parallel. This parallel combination is connected in series to a power supply and a resistor. The potential difference V between the ends of P is the same as the potential difference between the ends of Q.

The magnetic flux density at X due to the currents in the conductors is B.

It is suggested that B is related to p by the relationship B = YAV Lp + YZAV Lq

where Y and Z are constants.

Plan a laboratory experiment to test the relationship between B and p.

Draw a diagram showing the arrangement of your equipment.

Explain how the results could be used to determine values for Y and Z.

In your plan you should include: • 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. , ,

Diagram , , [15] , ,