Y12 Homework on Sankey Diagrams

Answers to calculations only.

Constructing Sankey Diagrams

1. An energy efficient light bulb is rated at 20W. It produces 5W of light. Calculate its efficiency and draw a Sankey Diagram to scale.

Efficiency = Useful power out/ power in x 100%

Eff= (5/20) x 100 = 25%

2. Paula transfers 40 000J of chemical energy during a race. She transfers 32 000J of heat energy to the surroundings during the race. Calculate her efficiency and draw a Sankey diagram to scale.

Efficiency = useful energy out/ energy in x 100%

Eff = 40 000 -32 000) /40000 = 8000/40000 = 0.2 =20%

3. Bradley does 1600J of work turning the pedals on his bike. 1577.6J is transferred to the rear sprockets. How much heat is lost and what is the efficiency of Bradley’s bike. Draw a Sankey diagram of Bradley’s chain

Efficiency = useful energy out/ energy in x 100%

Eff = 1577.6 / 1600 = 0.986 = 98.6%

4. The coal in Thomas’ boiler contains 40 kJ of energy. He loses 25.76kJ as heat as he puffs along a branch line. How efficient is Thomas and draw a Sankey diagram.

Efficiency = useful energy out/ energy in x 100%

Eff = (40 - 25.76)/40 = 0.356 = 35.6%

5. The fuel in Diesel’s tank contains 60kJ of chemical energy. He does 20.1kJ of work on the mainline. Calculate Diesel’s efficiency and draw a Sankey diagram.

Efficiency = useful energy out/ energy in x 100%

Eff = 20.1/60 = 0335 = 33.5%

6. The electric engine in Jeremy’s car can develop 3kW. If the car develops 2.658kW what is its efficiency.

 Efficiency = Useful power out/ power in x 100%

Eff = 2.658/3 = 0.886 = 88.6%

7. Jeremy dreams of a Ferrari Enzo which can develop a maximum of 700 bhp. (1 bhp = 750 Watts). Sadly for Jeremy cars are not very efficient. Typically, only about 30% of the energy that is available from the combustion of the petrol actually ends up overcoming friction to move the car forwards. Of the 70% of energy is that is not usefully converted, 55% may heat the cooling water that surrounds the engine block whilst  15% may be in the hot exhaust gases. To make car engines more efficient  the fuel has to burn at a higher temperature and the exhaust must be kept cooler. Draw a Sankey diagram of Jeremy’s dinosaur