A power station has a thermal efficiency of 38%. It generates 600 MW of electricity. (a) Calculate the total thermal input power needed. [2] (b) Calculate t...

(a) Total thermal input power

Efficiency is defined as the ratio of useful output power to total input power:

\(\text{efficiency} = \dfrac{\text{useful output power}}{\text{total input power}}\)

Rearranging:

\(\text{total input power} = \dfrac{\text{useful output power}}{\text{efficiency}} = \dfrac{600}{0.38}\) [1]

\(= 1579 \text{ MW} \approx 1580 \text{ MW}\) [1]

Only 38% of the thermal energy released by burning the fuel is converted into electricity; the rest is wasted.

(b) Rate at which energy is wasted

The wasted power is the difference between the total input and the useful output:

\(\text{wasted power} = 1580 - 600 = 980 \text{ MW}\) [1]

This large amount of waste energy is typically lost as heat to the surroundings through cooling towers or exhaust gases.

(c) Mass of coal burned per second

The coal releases 30 MJ of energy per kilogram. Converting the input power to joules per second:

\(1580 \text{ MW} = 1\,580\,000\,000 \text{ J/s}\)

\(\text{mass per second} = \dfrac{1\,580\,000\,000}{30 \times 10^{6}}\) [1]

\(= 52.7 \text{ kg/s} \approx 53 \text{ kg/s}\) [1]

The power station burns roughly 53 kg of coal every second to maintain its 600 MW electrical output.

(d) Two environmental problems caused by burning coal

Any two from:

• Carbon dioxide (CO₂) emissions contribute to global warming and climate change [1]
• Sulfur dioxide (SO₂) emissions cause acid rain, damaging ecosystems and buildings [1]
• Particulate emissions cause air pollution and respiratory health problems [1]
• Ash waste must be disposed of, potentially contaminating land and water [1]