Energy Sources (DP IB Physics: HL)

A tidal power station traps water when the tide rises above the level of the power station turbines. The trapped water is released in a controlled manner over a period of 7 hours.

The following data are available:

Difference between high and low tide water level = 3.0 m
Density of sea water = 1.1 × 10³ kg m^–3
Area of tidal basin = 250 km²
Overall efficiency of power station = 24% 

Calculate the mass of trapped water.

Determine the average loss of potential energy per second over the seven hours of controlled release of water.

For the tidal power station: 

[2]

[1]

A certain proportion of the water’s gravitational potential energy is transferred to the surroundings.

A horizontal-axis wind turbine with blades of length 12 m is sited in an area which has a reasonably constant average wind speed of 13 m s^–1 for significant parts of the day.

Calculate the average mass of air per second that passes through the area swept out by the blades of the turbine. Assume the density of air = 1.2 kg m⁻³.

The power which is available from this turbine is about 36% of the kinetic energy per second of the incident wind.

Calculate the output power available, in watts, at this wind speed from this generator.  

Outline the construction and operation of a horizontal-axis wind generator, by: 

[3]

[2]

Discuss reasons why this is the case. 

The Sizewell B Pressurised Water Reactor (PWR) in the UK uses Uranium-235 as fuel and water as both coolant and steam to drive a generator.

Outline the processes which lead to the production of thermal energy in the PWR.

A nuclear reactor has several key components. In generating electricity, outline the role of the:

[2]

[2]

Uranium–235 is the primary energy source in the PWR. It has an energy density in the region of 1.3 × 10¹⁸ J m^–3 and a specific energy of 7.0 × 10¹³J kg^–1.

[2]

[2]

If the overall efficiency of the power station is 37%, calculate the power output of the power station.

The diagram shows an arrangement of eight photovoltaic cells, which forms a single module. Each cell in the module has an emf of 0.75 V and an internal resistance of 1.9 Ω.

For the module, calculate:

[1]

[2]

The intensity of solar radiation incident on the module is 3.5 × 10² W m⁻². The photovoltaic cells are 22% efficient.

Calculate the minimum area required per module to fulfil the community’s energy needs.

The Sankey diagram shows the energy flow in a power station burning waste material to convert to heat which is then supplied through pipes to the homes and businesses of the local community.

For the power station: 

[2]

[2]

Another mechanism of heating water for use in the home uses solar heating panels.

Distinguish between a photovoltaic cell and a solar heating panel by referring to the operation of each and the energy transformations involved.

Pumped hydroelectric systems store water behind a dam. When electricity is needed in the grid the water is released to turn a turbine.

The system shown has an upper reservoir 42 m in depth when full and allows water to fall a vertical distance of 396 m before reaching the turbine.

Estimate the specific energy of the water held in the reservoir.

Water is made to flow out of the upper reservoir through connecting pipes at a rate of 12 000 m³ per minute. The density of water is 1.0 × 10³ kg m⁻³. 

Calculate the transfer rate of gravitational potential energy of the water stored in the reservoir.

The pumped storage system produces 0.62 GW of power and it can operate continuously for 22 hours before the water in the upper reservoir is depleted.

For the pumped storage system:

[1]

[2]

[1]

After the upper reservoir is drained it is refilled with water from the lower reservoir. Pumping this water uphill requires energy. 

Explain how the operating company makes a profit on the energy they sell to the National Grid.

A new model wind turbine has a blade of length 6000 cm and is positioned offshore where the wind speed is an average of 4.2 km hr⁻¹ and the air density is 1.2 × 10⁻⁶ g mm⁻³. 

Calculate the number of wind turbines required in the wind farm to power a town of 30 million houses for 2 years. 

An average household consumes 28.8 kWh of electricity in 1 day. 

Outline two assumptions made in calculating the power output of one turbine from part (a) and explain how each assumption simplifies your calculation. 

Analyse the validity of the two assumptions made in part (b)

In reality, wind turbines currently have a capacity factor of 60%

Capacity factor = 

Calculate the average wind speed for the actual output of the turbine. 

Show that the turbine is required to operate at the maximum possible wind speed for 14.4 hours a day to obtain a power output equivalent to the actual power output. 

A hydropower station in India has a semicircular dam of diameter 1.53 km and a depth of 53 m when full. The dam fills up during the monsoon season but is emptied at a steady rate over 8 days and 17 hours in the dry season. Water is released from the dam and falls a vertical distance of 305 m before reaching the turbine.   

The water has a density of 1.1 × 10³ kg m⁻³ and the efficiency of the power station is 31%.

Calculate the electrical power generated by the release of the water from the dam. 

Identify two ways that the hydropower station could increase its power output.

The Indian government are deciding if hydroelectric power would be a viable energy source to supply electricity to every household in the city of Mumbai during the dry season.

Some data is shown in the table below.

Using the data, calculate the number of dams that would be needed.

Comment on the suitability for Mumbai to use hydropower as its main energy source during the dry season, and give reasons for your answer.

Currently, 95% of the energy generated for the city of Mumbai comes from coal.

Suggest, with reasons, a cleaner and more sustainable alternative energy source for the Indian government to consider that would be more suitable for Mumbai. 

A small wind turbine with a blade length of 150 cm and an efficiency of 41% is situated in a field on the coast of Spain.

The air density at this location is 1200 g m⁻³. For 3.5 hours, the wind speed is 39.6 km hr⁻¹ and for 1.25 hours, the wind speed is 14.4 km hr⁻¹. 

Calculate the energy supplied by the wind turbine during this time.

A solar panel with a surface area of 1.45 × 10⁻⁶ km² and 44% efficiency is also present in the field.

The average intensity of sunlight received per day is 8.2 kWh m⁻², assuming that this location receives sunlight for an average of 8.2 hours per day.

Compare the energy supplied by the solar panel and the wind turbine when operating for the same number of hours.

The local council decide to install enough solar panels to power a village of 3500 houses. The average electricity consumption per household is 10.2 kWh per day. 

Pumped hydroelectric systems store water behind a dam. When electricity is needed in the grid the water is released to turn a turbine.

The system shown has an upper reservoir 42 m in depth when full and allows water to fall a vertical distance of 396 m before reaching the turbine.

Water, with a density of 1.0 × 10³ kg m⁻³, flows out of the reservoir at 1.5 × 10¹⁰ cm³ per minute. The pumped storage system produces 0.58 GW of power and can operate continuously for 19 hours and 27 minutes before the water in the upper reservoir is depleted. 

Calculate the efficiency, and hence, the total energy supplied by the system.

Draw a Sankey diagram to represent the energy transferred by the turbine in the hydroelectric dam, indicating clearly the scale used.

Distinguish between a solar heating panel and a photovoltaic cell using considerations of the energy transfers involved.

The holiday resort wishes to heat a 125-litre water tank from 10 °C to 40 °C over 2 hours to provide hot water for the chalet every 24 hours. The maximum amount of solar radiation incident upon the roof at any one time is 8.53 × 10⁻⁴ W mm⁻².

Water has a density of 1.1 × 10³ kg m⁻³ and a specific heat capacity of 4200 J kg °C⁻¹.

One photovoltaic cell is a rectangle of dimensions 500 mm and 300 mm. The power output of one cell is 215.36 W when radiation is at its maximum intensity.

The solar heating panel is 67% efficient. 

Compare the area on the roof required by the solar heating panels and the photovoltaic panels.

Justify the difference between the values calculated in part (b).