| Date | May 2014 | Marks available | 5 | Reference code | 14M.2.SL.TZ1.2 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Calculate, Identify, Show that, and State | Question number | 2 | Adapted from | N/A |
Question
This question is about a tidal power station.
A tidal power station is built for a coastal town. Sea water is stored in a tidal basin behind a dam at high tide and released in a controlled manner between high tides, so that it passes through turbines to generate electricity.
The following data are available.
Difference between high and low tide water level = 1.8m
Density of sea water = 1.1×103kgm–3
Surface area of basin = 1.4×105m2
Overall efficiency of power station = 24%
(i) Show that the mass of sea water released between successive high and low tides is about 2.8×108 kg.
(ii) Calculate the electrical energy produced between successive high and low tides.
(i) Identify one mechanism through which energy is transferred to the surroundings during the electricity generation process.
(ii) State why the energy transferred to the surroundings is said to be degraded.
Markscheme
(i) m = ρΔV = ρAΔh;
=1.1×103 ×1.4×105 ×1.8;
(≈ 2.8×108 kg)
(ii) difference in height of centre of mass of water=\(\frac{{1.8}}{2}\)=0.9(m)
\(\Delta {E_P}\left( { = mg\Delta h = 2.8 \times {{10}^8} \times 9.8 \times 0.9} \right) = 2.5 \times {10^{\rm{9}}}\left( {\rm{J}} \right)\)
electrical energy (=0.24×2.5×109)=5.9×108 (J)(=590MJ);
Allow ECF for [2 max] if candidate omits factor of 2 in first marking points. Accept g=10ms–2 giving an answer of 6.0×108 (J).
(i) friction/turbulence of flowing water / friction in turbine/generator / resistive heating in wires;
Do not allow bald statement of “heating”.
(ii) it can no longer be used to do work / not available in useful form;
Do not accept “it is more spread out” or similar.
Examiners report
ai) Many candidates provided a simple calculation with no explanation to show why the values were multiplied together. This did not provide sufficient evidence to show how the data provided lead to the given value.
aii) Few candidates realized that the energy produced by a water storage is dependent on half the height between the upper and lower water levels.
bi) Many candidates provided a general response such as “friction” without identifying the mechanism that caused the frictional losses.
bii) Few candidates could adequately explain the concept of degraded energy.
