Assertion (A) : The work output of SI engines can be improved by increasing the compression ratio. Reason (R) : Fuels of higher octane number can be employed at higher compression ratio. Select the correct answer.
Both (A) and (R) are true but (R) is not correct explanation of (A)
Analyzing the Assertion and Reason regarding SI Engines
The question presents an Assertion (A) and a Reason (R) related to Spark Ignition (SI) engines, compression ratio, and fuel octane number. We need to evaluate if each statement is true and if the Reason correctly explains the Assertion.
Understanding Assertion (A): Work Output and Compression Ratio
Assertion (A): The work output of SI engines can be improved by increasing the compression ratio.
In thermodynamic cycles like the ideal Otto cycle, which is a model for SI engines, the thermal efficiency is given by:
\[ \eta_{\text{thermal}} = 1 - \frac{1}{r^{\gamma-1}} \]Where:
- \( \eta_{\text{thermal}} \) is the thermal efficiency.
- \( r \) is the compression ratio.
- \( \gamma \) is the ratio of specific heats (\( c_p / c_v \)) of the working fluid.
This formula shows that increasing the compression ratio \( r \) (assuming \( \gamma > 1 \)) increases the thermal efficiency. Thermal efficiency is related to the work output by:
\[ \eta_{\text{thermal}} = \frac{\text{Work Output}}{\text{Heat Input}} \]For a given amount of fuel (heat input), a higher thermal efficiency means a higher work output. Therefore, increasing the compression ratio generally improves the work output of an SI engine.
Based on this, Assertion (A) is true.
Understanding Reason (R): Octane Number and Compression Ratio
Reason (R): Fuels of higher octane number can be employed at higher compression ratio.
In SI engines, knocking or detonation is a major concern, especially at higher compression ratios. Knocking occurs when the unburnt fuel-air mixture spontaneously ignites ahead of the flame front, leading to rapid pressure rise and potentially engine damage.
The octane number of a fuel is a measure of its resistance to knocking. Fuels with a higher octane number have a greater resistance to auto-ignition. Therefore, using fuels with a higher octane number allows engines to operate safely at higher compression ratios without experiencing knocking.
Based on this, Reason (R) is true.
Evaluating the Relationship between (A) and (R)
Both Assertion (A) and Reason (R) are true statements. Now we need to determine if (R) is the correct explanation for (A).
(A) states that higher compression ratio improves work output because it increases thermal efficiency (as per thermodynamic principles). (R) states that higher octane fuel allows the use of higher compression ratios by preventing knocking.
Reason (R) explains *why* it is possible to *implement* higher compression ratios in practice (by using appropriate fuel), which then leads to the improved work output mentioned in (A). However, (R) does not explain *how* increasing the compression ratio itself improves work output. The improvement in work output is a direct consequence of the thermodynamic efficiency gain associated with the higher compression ratio, independent of the fuel's octane rating.
Think of it this way: High octane fuel is an enabler for higher compression ratios, and higher compression ratios enable higher work output. But the octane fuel itself does not cause the higher work output; the higher compression ratio does. Reason (R) explains a condition necessary for achieving the state described in (A) safely, but not the fundamental physical principle behind (A).
Therefore, while both statements are true, Reason (R) is not the correct explanation for Assertion (A).
Conclusion
Assertion (A) is true, and Reason (R) is true, but Reason (R) is not the correct explanation of Assertion (A).
This corresponds to Option 2.
Important Questions from Otto Cycle
The thermal efficiency of a standard Otto cycle for a compression ratio of 5.5 will be -
Otto cycle is a constant ________ cycle.
In an air standard Otto cycle, the compression ratio is 7. Find the cycle efficiency
Which of the following statements is incorrect?
Which of the following cycle is used in spark ignition (SI) engine?
