Question

Thermal efficiency of a spark ignition engine increases with the increase of

• A. compression ratio
• B. speed
• C. atmospheric temperature
• D. cylinder dimensions

Hint:

For both Otto and Diesel cycles, increasing the compression ratio increases the theoretical thermal efficiency.
This is the most effective design variable for improving engine efficiency.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A Spark Ignition (SI) engine operates on the theoretical Otto cycle.
The thermal efficiency (\( \eta \)) of this cycle represents the fraction of heat energy converted into useful mechanical work.
This efficiency is governed by thermodynamic relationships involving the volume changes during the compression stroke.
Key Formula or Approach:
The theoretical thermal efficiency of the air-standard Otto cycle is given by the formula:
\[ \eta = 1 - \frac{1}{r^{\gamma - 1}} \]
where:
- \( r \) is the compression ratio of the engine.
- \( \gamma \) is the adiabatic index (ratio of specific heats, \( C_p / C_v \)), which is approximately \( 1.4 \) for air.

Step 2: Detailed Explanation:
Let us analyze how the parameters affect the thermal efficiency using our equation:
1. The compression ratio (\( r \)) is defined as the ratio of the maximum cylinder volume (when the piston is at Bottom Dead Center, BDC) to the minimum cylinder volume (when the piston is at Top Dead Center, TDC):
\[ r = \frac{V_s + V_c}{V_c} \]
where \( V_s \) is the swept volume and \( V_c \) is the clearance volume.
2. According to our efficiency formula, as the compression ratio (\( r \)) increases, the term \( r^{\gamma - 1} \) in the denominator also increases.
3. This causes the fraction \( \frac{1}{r^{\gamma - 1}} \) to decrease.
4. Subtracting a smaller fraction from 1 results in a higher thermal efficiency (\( \eta \)).
Physically, a higher compression ratio allows the fuel-air mixture to be compressed to a smaller volume, leading to higher combustion temperatures and pressures, which increases the work output per unit of fuel consumed.
In SI engines, the compression ratio is limited to approximately \( 6 \) to \( 10 \) to prevent premature auto-ignition (knocking).
Speed, atmospheric temperature, and overall cylinder dimensions do not directly govern the theoretical thermal efficiency of the cycle.

Step 3: Final Answer:
The thermal efficiency increases with the increase of the compression ratio.