A student investigates how the viscous force in a liquid varies with temperature. The student releases a ball from the surface of the liquid in a container. The ball falls as shown in Fig. 2.1. [Figure 2.1] The student determines the speed of the ball between P and Q and measures the thermodynamic temperature T of the liquid. Viscosity is a term used to describe the viscous forces acting in a liquid. Viscosity has the unit pascal second (Pa s). The viscosity η of the liquid is calculated from the speed of the ball. The experiment is repeated for the same liquid at different temperatures. It is suggested that η and T are related by the equation η = He^(E/(kT)) where E and H are constants and k is the Boltzmann constant.

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

1. [1] gradient = E / k
2. [1] y-intercept = In H
3. [1] In (η / 10⁻⁴ Pa s)
4. 2.510 or 2.5096
5. 2.28 or 2.282
6. 2.13 or 2.128
7. 1.92 or 1.917
8. 1.72 or 1.723
9. 1.57or 1.569
10. [1] Absolute uncertainties in In η from ± 0.02 (or ± 0.016) to about ± 0.04
11. [1] Six points plotted correctly. Must be accurate to nearest half a small square. Diameter of points must be less than half a small square.
12. [1] Error bars in In η plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical.
13. [1] Line of best fit drawn. Points must be balanced. Do not accept top point to bottom point. Line must pass between (2.93, 1.65) and (2.96, 1.65) and between (3.38, 2.45) and (3.41, 2.45).
14. [1] Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted.
15. [1] Gradient determined with clear substitution of data points into Δy / Δx. Distance between data points must be at least half the length of the drawn line.
16. [1] uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
17. [1] y-intercept determined from substitution into y = mx + c.
18. [1] E determined using gradient and given to two or three significant figures. Correct substitution of numbers required. E = 1.38 × 10⁻²³ × gradient = 1.38 × 10⁻²³ × (c)(iii)
19. [1] H determined using y-intercept. H = eʸ⁻ᶦⁿᵗᵉʳᶜᵉᵖᵗ = e⁽ᶜ⁾⁽ⁱᵛ⁾ (× 10⁻⁴)
20. [1] E determined using gradient and H determined using y-intercept and dimensionally correct units for E (J) and H (Pa s).
21. [1] ΔE = 1.38×10⁻²³ × absolute uncertainty in gradient or ΔE = (Δgradient / gradient) × E
22. [1] η determined from (d)(i) or (c)(iii) and (c)(iv) with correct substitution shown and correct power of ten.
23. η = H × e^(E/(kT)) = e⁽ᶜ⁾⁽ⁱᵛ⁾ ×10⁻⁴ × e^(E/(1.38×10⁻²³×273))
24. or η = e^(y-intercept) ×10⁻⁴ × e^(gradient/273)
25. or η = e⁽ᶜ⁾⁽ⁱᵛ⁾ × 10⁻⁴ × e^((c)(iii)/273)
26. or ln η = E/(kT) + ln H = (d)(i)/(1.38×10⁻²³×273) + (c)(iv)
27. or ln η = gradient/273 + y-intercept = (c)(iii)/273 + (c)(iv)