03.1 Explain what is meant by an adiabatic change - AQA - A-Level Physics - Question 3 - 2022 - Paper 6

The compression ratio, defined as V1/V2, can be calculated using the formula for adiabatic processes:

$\frac{P_1}{P_2} = \left( \frac{V_2}{V_1} \right)^{\gamma}$

Where:

• P1 (initial pressure) = 1.0 × 10^5 Pa
• P2 (final pressure) = 67 × 10^5 Pa

From the above relationship, we can rearrange to find:

$\frac{V_1}{V_2} = \left( \frac{P_2}{P_1} \right)^{\frac{1}{\gamma}}$

Substituting in the values:

$\frac{V_1}{V_2} = \left( \frac{67 \times 10^5}{1.0 \times 10^5} \right)^{\frac{1}{1.4}}$ $\frac{V_1}{V_2} = 67^{\frac{1}{1.4}} \approx 20.27$

Diesel engines require a higher compression ratio to achieve a sufficiently high temperature to ignite the fuel. Unlike petrol engines, which rely on spark ignition, diesel engines compress air to very high pressures and temperatures before injecting the fuel, which ignites due to the high temperature. Thus, a higher compression ratio is essential for diesel engines to ensure that the combustion occurs efficiently under lower pressures and temperatures.

In this figure, the indicator diagram should represent the characteristic loop of a diesel engine cycle, showing a curve that reflects the pressure change at constant volume and varying volume at fixed pressure stages. The loop would typically demonstrate a rising pressure followed by a more gradual decline, with areas indicating work done during expansion and compression phases.

The marking should be placed near the point in the diagram where the curve begins to rise significantly, indicating the start of the fuel injection phase in the diesel cycle.

The ideal cycle assumes constant values throughout the process and does not account for the real engine's inefficiencies, such as heat loss or incomplete combustion. In contrast, the indicator diagram will show a more complex curve with hysteresis that reflects the real conditions in the engine, including valve timing, friction, and other thermodynamic losses. This complexity results in a shape that diverges from the smoother ideal cycle representation.