8.1 Energy Sources

What is the efficiency of a system whose Sankey diagram is shown below?

The Sankey diagram is drawn to scale.

A coal-fired power station with an efficiency ε burns fuel that has an energy density D and a specific energy S. The rate at which the mass of the fuel is consumed is M.

What is the power output of the power station? 

Which adaptation to a wind turbine produces the largest increase in its maximum possible theoretical power output?

Burning 1 kg of coal produces less energy than burning 1 litre of gasoline. The density of gasoline is 1 g cm⁻³. 

Which option is correct?

In a nuclear reactor, a chain reaction is produced and controlled. Uranium-235 is the isotope used in many nuclear reactors.

Which of the following statements is incorrect?

A wind turbine of blade length r  m has wind of a speed v  m s⁻¹ and air density ρ incident on its blades. 

Which expression shows the power obtained by the wind turbine every second? 

The following nuclear fusion reaction is taking place in a nuclear reactor: 

The following data is available: 

• The mass defect ≈ 0.02 u
• Atomic mass unit, u ≈ 2.0 × 10⁻²⁷ kg
• Number of seconds in a year = 3 × 10⁷

What is an estimate of the number of such fusion reactions required to keep an average household, which uses approximately 24 000 kWh of electrical energy per year, running for a year? 

Burning 1000 kg of coal can yield 3 × 10¹⁰ J of energy. When a thermal neutron is absorbed by a uranium-235 nucleus it produces fission products as well as three neutrons. 

The following data is available:

• Mass defect ≈ 0.2 u
• Mass of  ≈ 4 × 10⁻²⁵ kg
• Atomic mass unit, u ≈ 2.0 × 10⁻²⁷ kg

What is an estimate of the mass of coal needed to give the same amount of energy as 1 kg of Uranium-235?

A solar panel has a surface area of 2.5 m² and an efficiency of 25 %. The average intensity of sunlight received per day is 8 kWh m⁻²  for an average of 10 hours per day. 

The average electricity consumption per factory is 100 kWh per day on an industrial estate of five factories where each factory is in operation for 20 hours each day. 

How many solar panels are needed to power the industrial estate for one day?

Diesel fuel has a specific energy of about 4.5 × 10⁷ J kg⁻¹ and an energy density of close to 3.5 × 10¹⁰ J m⁻³. Which value is closest to the density of diesel?

The Sankey diagram shows the energy transformations in a laptop computer while a person is watching a film.

What is the efficiency of the laptop?

Possible energy sources used in power stations are

1. coal
2. biofuel
3. nuclear fuel
4. water released from natural reservoirs

Which of these are primary sources of energy?

Which line in the table correctly shows a renewable and a non-renewable energy, and a major direct use for both energy sources?

Horizontal-axis wind turbines convert a proportion of the kinetic energy of the wind incident on the propeller into kinetic energy of the rotating blades. The conversion cannot be 100 % because:

An array of photovoltaic cells is set up so that 20 solar cells are connected together as shown. Each cell has an output of 12 V and 2.5 A.

What is the potential difference and the current output of the array?

What is an advantage of pumped storage systems?

A wind turbine has a power output P when the wind speed is v. What is the wind speed when the power output is reduced to P if the efficiency is not affected?

An arrangement of wind turbines is shown, with four possible directions of wind.

Which orientation of the turbines to the wind will allow the maximum energy to be generated from this wind farm?