A student investigates the heating of a solid metal cylinder. Fig. 1.1 shows the cylinder of cross-sectional area A and height h. h A cylinder Fig. 1.1 The student places the cylinder and an electrical heater in a beaker of water. The electrical heater is switched on and the student measures the time t for the temperature of the water to increase by Δθ. A number of cylinders of the same material but with different cross-sectional areas are available. It is suggested that the relationship between t and A is Pt = AhWΔθ + ZΔθ where P is the power of the heater and W and Z are constants. Design a laboratory experiment to test the relationship between t and A. Explain how your results could be used to determine values for W and Z. 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.

Mark scheme

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

1. A is the independent variable and t is the dependent variable or vary A and measure t
2. keep Δθ constant
3. labelled diagram of workable experiment including: beaker of water, cylinder in water, electrical heater in water, thermometer in water, minimum of three labels from heater, thermometer, cylinder, water, beaker
4. circuit diagram to determine power of the heater e.g. ammeter and voltmeter correctly positioned with a power supply or wattmeter correctly connected to power supply and heater
5. method to determine time for temperature of water to increase or t, e.g. use a stopwatch/timer
6. method to determine A, e.g. micrometer/calipers to determine diameter of cylinder and A = πd²/4
7. plot a graph of t against A (not logarithmic graphs)
8. W = gradient × P / hΔθ
9. Z = y-intercept × P / Δθ
10. D1 wear (heat proof) gloves to prevent burns from hot beaker/cylinder/heater/water
11. D2 keep P and h constant
12. D3 check that/ensure/keep initial temperature of the water constant or volume/mass of water constant
13. D4 use calipers/ruler to measure h
14. D5 repeat measurements of diameter in different directions/at different positions along cylinder and average
15. D6 method to calculate power of heater e.g. P = VI linked to correct circuit diagram for ammeter/voltmeter method
16. D7 repeat measurements of t for same A and average t
17. D8 ensure heater and cylinder are (totally) submerged/immersed or stir water (using a glass rod/stirrer)
18. D9 relationship valid if a straight line (not passing through the origin)
19. D10 method to insulate beaker, e.g. use of a lid on the beaker or foam/insulation around outside of beaker