Thermal Engineering, Refrigeration & Power

Spark ignition (petrol/gasoline) engines operate on the Otto cycle and are constrained by the self-ignition temperature of the fuel-air mixture. To prevent premature auto-ignition (knocking or detonation), their compression ratios are kept relatively low, traditionally ranging from $5\text{ to }8$ (modern petrol engines up to $10 - 12$). In comparison, compression ignition (diesel) engines operate at much higher ratios of $15\text{ to }22$.

Option analysis:

• $3\text{ to }6$: Too low for efficient internal combustion.
• $5\text{ to }8$: Correct, standard classical textbook compression ratio range for petrol engines.
• $15\text{ to }20$: Typical compression ratio range for diesel engines.
• $30\text{ to }40$: Exceedingly high, structurally and thermodynamically unviable.

In reciprocating internal combustion engines, the compression ratio ($r$) is defined as the ratio of the total cylinder volume when the piston is at Bottom Dead Centre (BDC) to the clearance volume when the piston is at Top Dead Centre (TDC):

Option analysis:

• $\frac{\text{Total volume}}{\text{Swept volume}}$: Incorrect denominator.
• $\frac{\text{Total volume}}{\text{Clearance volume}}$: Correct standard definition of engine compression ratio.
• $\frac{\text{Swept volume}}{\text{Total volume}}$: Inverted relationship.
• $\frac{\text{Clearance volume}}{\text{Swept volume}}$: Inverted fraction.

According to the Parallelogram Law of Forces, when two coplanar forces $P$ and $Q$ act simultaneously on a particle with an angle $\theta$ between their lines of action, the magnitude of their resultant force $R$ is given by:

Option analysis:

• $R = \sqrt{P^2 + Q^2 + 2PQ\sin 2\theta}$: Incorrect trigonometric term.
• $R = \sqrt{P^2 + Q^2 + 2PQ\cos\theta}$: Correct parallelogram law formula.
• $R = \sqrt{P^2 + Q^2 - 2PQ\sin\theta}$: Incorrect sign and function.
• $R = \sqrt{P^2 + Q^2 + 2PQ\cos 2\theta}$: Incorrect angle argument.