Outline in terms of energy changes how electrical energy is obtained from the energy of wind.

Air of density ρ and speed v passes normally through a wind turbine of blade length r as shown below.

(i) Deduce that the kinetic energy per unit time of the air incident on the turbine is

\[\frac{1}{2}\pi \rho {r^2}{v^3}\]

(ii) State two reasons why it is impossible to convert all the available energy of the wind to electrical energy.

Air is incident normally on a wind turbine and passes through the turbine blades without changing direction. The following data are available.

Density of air entering turbine = 1.1 kg m^–3
Density of air leaving turbine = 2.2 kg m^–3
Speed of air entering turbine = 9.8 m s^–1
Speed of air leaving turbine = 4.6 m s^–1
Blade length = 25 m

Determine the power extracted from the air by the turbine.

A wind turbine has a mechanical input power of 3.0×10⁵W and generates an electrical power output of 1.0×10⁵W. On the grid below, construct and label a Sankey diagram for this wind turbine.

Outline one advantage and one disadvantage of using wind turbines to generate electrical energy, as compared to using fossil fuels.

Advantage:

Disadvantage:

kinetic energy of wind transferred to (rotational) kinetic energy of turbine/blades;
kinetic energy changed to electrical energy in generator/dynamo;
Generator/dynamo must be mentioned.

(i) volume of cylinder of air passing through blades per second =vπr²;
mass of air incident per second=ρvπr²;
kinetic energy per second= \(\frac{1}{2}m{v^2}\);
leading to \(\frac{1}{2}\pi \rho {r^2}{v^3}\)
Award [3] for answers that combine one or more steps.

(ii) the speed of the air/wind cannot drop to zero;
wind turbulence / frictional losses in turbine/any moving part / resistive
heating in wires;

kinetic energy per second of air entering turbine \( = \frac{1}{2}\pi  \times 1.1 \times {25^2} \times {9.8^3} = 1.016 \times {10^6}\);
kinetic energy per second of air leaving turbine \( = \frac{1}{2}\pi  \times 2.2 \times {25^2} \times {4.6^3} = 2.102 \times {10^5}\);
power extracted \( = 1.0 \times {10^6} - 2.1 \times {10^5} = 8.062 \times {10^5} \approx 8.1 \times {10^5}{\rm{W}}\);

correct shape of diagram (allow multiple arrows if power loss split into different components);
relative width of arrows correct;
labels correct;

Advantage:
wind is renewable so no resources used up / wind is free / no chemical pollution / no carbon dioxide emission / does not contribute to greenhouse effect / is “scalable” i.e. many sizes of turbine possible;

Disadvantage:
expensive initial cost / large land area needed / wind not constant / effect on movement of birds / aesthetically unpleasant / noise pollution / high maintenance costs / best locations far from population centres / low energy density;

Accept any other suitable advantage or disadvantage.