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Date May 2018 Marks available 1 Reference code 18M.2.SL.TZ2.5
Level Standard level Paper Paper 2 Time zone 2
Command term Suggest Question number 5 Adapted from N/A

Question

In a pumped storage hydroelectric system, water is stored in a dam of depth 34 m.

M18/4/PHYSI/SP2/ENG/TZ2/05

The water leaving the upper lake descends a vertical distance of 110 m and turns the turbine of a generator before exiting into the lower lake.

Water flows out of the upper lake at a rate of 1.2 × 105 m3 per minute. The density of water is 1.0 × 103 kg m–3.

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

[2]
a.i.

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

[3]
a.ii.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

[1]
a.iii.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

[1]
b.

Markscheme

Average height = 127 «m»

Specific energy «= m g h ¯ m = g h ¯ = 9.81 × 127» = 1.2 × 103 J kg–1

 

Unit is essential

Allow g = 10 gives 1.3 × 103 J kg–1

Allow ECF from 110 m

(1.1 × 103 J kg–1) or 144 m

(1.4 × 103 J kg–1)

[2 marks]

a.i.

mass per second leaving dam is 1.2 × 10 5 60  × 103«2.0 × 106 kg s–1»

rate of decrease of GPE is = 2.0 × 106 × 9.81 × 127

= 2.49 × 109 «W» /2.49 «GW»

 

Do not award ECF for the use of 110 m or 144 m

Allow 2.4 GW if rounded value used from (a)(i) or 2.6 GW if g = 10 is used

[3 marks]

a.ii.

efficiency is « 1.8 2.5 =» 0.72 / 72%

[1 mark]

a.iii.

water is pumped back up at times when the demand for/price of electricity is low

[1 mark]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
a.iii.
[N/A]
b.

Syllabus sections

Core » Topic 8: Energy production » 8.1 – Energy sources
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