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

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

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

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.

Average height = 127 «m»

Specific energy «= \(\frac{{mg\bar h}}{m} = g\bar h\) = 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]

mass per second leaving dam is \(\frac{{1.2 \times {{10}^5}}}{{60}}\) × 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]

efficiency is «\(\frac{{1.8}}{{2.5}}\) =» 0.72 / 72%

[1 mark]

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

[1 mark]