Energy Resources and Energy Transfers

6 marks · Normal

In a hydroelectric power station, water of mass 2.0 × 10^5 kg falls from a height of 50 m every minute to turn the turbines. The electrical power output of the station is 1.0 MW (1.0 × 10^6 W). Assume g = 10 N/kg.

(a)

Calculate the total gravitational potential energy lost by the water each minute.

[2 marks]

(b)

How much electrical energy is produced by the station each minute?

[2 marks]

(c)

Calculate the efficiency of the power station.

[2 marks]

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(a) 1.0 × 10^8 J

(b) 6.0 × 10^7 J

Common mistakes: Not converting minutes to seconds

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Marking points

M1 (a) · 1 mark · Substitutes correct values into GPE = mgh (follow-through)

A1 (a) · 1 mark · Gives correct result in J (follow-through)

M2 (b) · 1 mark · Recognises electrical energy = electrical power × time (follow-through)

A2 (b) · 1 mark · Correctly calculates electrical energy in J (follow-through)

M3 (c) · 1 mark · Uses efficiency = useful output / input × 100% (follow-through)

A3 (c) · 1 mark · Correct percentage (accept 59–61%) (follow-through)

Worked solution