Otto Cycle Air Standard Efficiency Formula
The air standard efficiency of an Otto Cycle is a theoretical measure used to evaluate the performance of spark-ignition internal combustion engines. It is based on the ideal Otto cycle, assuming air as the working substance undergoing specific thermodynamic processes.
Key Formula
The expression for the air standard efficiency ($\eta_{otto}$) of an Otto Cycle is directly related to the compression ratio (r) and the ratio of specific heats for air (gamma, $\gamma$). The standard formula is:
$ \eta_{otto} = 1 - \frac{1}{r^{\gamma-1}} $
Explanation of Terms
- r: Compression ratio (the ratio of the volume after compression to the volume before compression).
- $\gamma$: Adiabatic index or ratio of specific heats ($C_p / C_v$) for the working fluid (air). For air, $\gamma \approx 1.4$.
Analysis of Options
Comparing the standard formula with the given options:
- Option 1: $\eta_{otto} = 1 - [\frac{\gamma-1}{(r)^{\gamma-1}}]$ - Incorrect.
- Option 2: $\eta_{otto} = 1 - [\frac{1}{(r)^{1-\gamma}}]$ - Incorrect exponent term.
- Option 3: $\eta_{otto} = 1 - [\frac{1}{(r)^\frac{\gamma-1}{\gamma}}]$ - Incorrect exponent term.
- Option 4: $\eta_{otto} = 1 - [\frac{1}{(r)^{\gamma-1}}]$ - Matches the standard formula.
Therefore, the correct expression for the air standard efficiency of the Otto Cycle is $1 - [\frac{1}{(r)^{\gamma-1}}]$.
Important Questions from IC Engine Cycles
- The indicated thermal efficiency of an internal combustion engine is defined as:
In a four-stroke cycle, the minimum temperature inside the engine cylinder occurs at the
The working cycle of two stroke engine is completed in _______ revolutions of crank shaft.
The ratio between net work for one cycle in a process and displacement volume is -
The fourth stage of the compression ignition process is:
