Engine cycles

State what is meant by an isothermal change.

Figure 6 shows a p – V diagram in which a fixed mass of an ideal gas is taken through a cycle of three processes.

A → B: adiabatic change B → C: isothermal change C → A: reduction in volume at constant pressure

The maximum temperature of the gas in the cycle is 536 K and the minimum temperature is 291 K.

Calculate, in mol, the amount of gas.

Show that the work done in process C → A is about 100 J.

Complete Table 2 for each process and for the whole cycle.

Two criteria for a heat engine to achieve the maximum theoretical efficiency are:

1. the gas must always be at the same temperature as the hot source when energy is being transferred to the gas by heat transfer

2. the gas must always be at the same temperature as the cold sink when energy is being transferred from the gas by heat transfer.

The temperatures of the source and sink do not change.

Deduce whether the cycle in Figure 6 satisfies either or both of these criteria.

The overall efficiency of a heat engine is defined as

An engineer suggests designing a real engine based on the cycle shown in Figure 6.

Discuss the engineer’s suggestion.

In your answer you should:

• use Table 2 to determine the overall efficiency of a theoretical engine that uses the cycle

• compare this overall efficiency with the efficiency of an ideal engine working between the same temperatures as the cycle

• discuss with reasons the problems that would need to be overcome in making a real engine work on this cycle

• explain whether the engineer’s suggestion would lead to a useful engine.

The Lenoir engine was the first successful internal combustion engine.

Figure 6 shows the basic form of the Lenoir engine. The piston rod drives a crankshaft which is not shown. The fuel is a mixture of gas and air.

Figure 7 shows an indicator diagram for the space L, taken during a test on a Lenoir engine.

In one cycle the following changes occur in L.

• Induction. The piston starts at the left-hand end of the cylinder. It moves to the right and fuel passes through the open inlet valve V₁ into L. Figure 6 shows the piston during this induction process, with V₁ open.

• Ignition. When the piston is nearly halfway along the cylinder, V₁ is closed. A spark ignites the fuel causing a sudden rise in pressure.

• Expansion. The hot gases expand and the piston moves to the end of the stroke.

• Exhaust. The exhaust valve V₂ opens. The piston moves to the left. The exhaust gases are expelled at atmospheric pressure.

The same processes are repeated in space R one half of a revolution of the crankshaft later than in L. So when the piston is moving to the left, induction, ignition and expansion occur in R at the same time as the exhaust process occurs in L.

The indicator diagram is for a rotational speed of the crankshaft of 120 rev min⁻¹.

Determine, using Figure 7, the indicated power of the engine. Assume that the indicator diagram for R is identical to the indicator diagram for L.

The following data are taken during the test on the engine:

Calculate the input power and the output (brake) power of the engine.

The output power of a four-stroke petrol engine of a similar working volume to that of the Lenoir engine is about 150 kW.

Suggest two reasons for the very low output power of the Lenoir engine compared with a four-stroke petrol engine.

Which statement is correct?

Tick () one box.

Figure 7 shows the p – V diagram for a theoretical diesel engine cycle. Figure 8 shows the indicator diagram for a real four-stroke diesel engine working between the same maximum and minimum volumes.

Compare the indicator diagram with the theoretical diesel cycle. In your answer, explain:

• the differences between region A on Figure 7 and region A on Figure 8

• the differences between region B on Figure 7 and region B on Figure 8

• why the features shown in region C appear only on the indicator diagram

• why the efficiency of the real engine will always be less than the efficiency predicted by an analysis of the theoretical cycle.

Explain what is meant by an adiabatic change.

Figure 4 shows the p – V diagram for an ideal diesel engine cycle.

In this cycle, air is compressed adiabatically from a pressure of 1.0 × 10⁵ Pa and volume V₁ to a pressure of 67 × 10⁵ Pa and volume V₂. The adiabatic index γ for air = 1.4 Calculate the compression ratio .

Explain why the compression ratio for a diesel engine must be greater than the compression ratio for a petrol engine.

The dashed lines in Figure 5 show the p – V diagram for the ideal diesel engine cycle.

Draw, on Figure 5, a typical indicator diagram for a real four-stroke diesel engine with

Mark with an X on your diagram the point where the injection of fuel starts.

Explain two differences between the ideal cycle and the indicator diagram for the real engine.

Figure 4 shows the results of a test on an internal combustion engine which uses purified biogas.

Figure 4 shows how the indicated power, brake (or output) power and fuel consumption of the engine vary with the engine speed. The scale on the left-hand axis is power and the scale on the right-hand axis is fuel consumption.

Figure 4 can be used to analyse the performance of the engine.

Determine, for the speed at which the engine develops its maximum brake power:

• the overall efficiency

• the thermal efficiency

• the mechanical efficiency.

Go on to explain how knowledge of these efficiencies can be useful to an engineer.

calorific value of biogas used in the test = 32.3 × 10⁶ J m⁻³

Explain why it is not advisable to run this engine at speeds above 7000 rev min⁻¹. Refer to Figure 4 in your answer.

Figure 4 shows some of the equipment used to investigate the thermal and mechanical efficiencies of a single-cylinder four-stroke petrol engine.

• Petrol is supplied to the engine from a calibrated reservoir.

• Sensors are used to measure the volume V and pressure p above the piston inside the cylinder.

• The dynamometer applies a load to the output shaft and measures the output torque of the engine.

• The tachometer measures the rotational speed of the engine in revolutions per second.

In one test the air intake valve (throttle) setting remains fixed and the load provided by the dynamometer is kept constant.

Describe how you would determine the input power, the indicated power, the brake power, the thermal efficiency and the mechanical efficiency.

In your answer you should

• describe the measurements that you would take

• show how you would use the measurements and any other necessary data.

A turning moment diagram is a graph showing the variation of torque produced by an engine or motor with the angle of rotation of the output shaft.

Figure 2 shows the turning moment diagrams for a single-cylinder diesel engine and an electric motor that have the same output power.

State what is represented by the area between the curve and the angle axis for a turning moment diagram.

The diesel engine or the electric motor may be used to drive a machine that has a low moment of inertia and that requires an almost constant torque.

Discuss why, to drive this machine, the diesel engine would need to be fitted with a flywheel.

In your answer you should explain

• why the electric motor does not require a flywheel

• why the torque of the diesel engine varies over one cycle, including why there are points where the torque is zero

• how the moment of inertia of the flywheel influences the motion of the output shaft of the diesel engine.

Figure 3 shows the p – V diagram for an idealised diesel engine cycle. In this cycle a fixed mass of air is taken through four processes 1 2 3 4 1.

Which statement about this cycle is true? Tick (✓) the correct answer.

The cycle in Figure 3 may be modified by allowing the air to continue to expand adiabatically from state 4 until it is at atmospheric pressure at state 5. Figure 4 shows the modified cycle.

The expansion stroke 3 5 is now longer than the compression stroke 1 2. Process 5 1 takes place at constant pressure.

It has been claimed that, compared to the cycle in Figure 3, the modified cycle of Figure 4 gives

A an increase in work done per cycle of 130 J B an increase in efficiency of more than 15%

Deduce whether these claims are true.

Claim A

Claim B

For the air in process 5 1 in Figure 4, ΔU = –374 J

Calculate the energy that must be removed by cooling for process 5 1.

0.060 mol of air is taken through the cycle.

Determine the maximum temperature in the cycle.

maximum and minimum volumes.

Compare the theoretical and real engine cycles. In your answer you should:

state and explain the differences between the cycles

explain why the work output per cycle of the real engine is less than that predicted by an analysis of the theoretical cycle.