Question

Compression ratio is defined as the ratio of:

• A. \(\frac{\text{total volume}}{\text{swept volume}}\)
• B. \(\frac{\text{total volume}}{\text{clearance volume}}\)
• C. \(\frac{\text{swept volume}}{\text{total volume}}\)
• D. \(\frac{\text{clearance volume}}{\text{swept volume}}\)

Hint:

Always remember: the compression ratio is the ratio of the maximum cylinder volume (when the piston is all the way down) to the minimum cylinder volume (when the piston is all the way up):
\[ r = \frac{\text{Maximum Volume}}{\text{Minimum Volume}} = \frac{V_{\text{total}}}{V_{\text{c}}} \]

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The compression ratio (\(r\)) is a key geometric parameter that determines the thermodynamic efficiency of internal combustion engines.
It is calculated by comparing the cylinder volumes at the beginning and the end of the compression stroke.
Key Formula or Approach:
The cylinder volume consists of two parts:
- Swept volume (\(V_{\text{s}}\)): The volume swept by the piston as it moves from BDC to TDC.
- Clearance volume (\(V_{\text{c}}\)): The volume remaining in the cylinder when the piston is at TDC.
The total cylinder volume (\(V_{\text{total}}\)) is the sum of these volumes:
\[ V_{\text{total}} = V_{\text{s}} + V_{\text{c}} \]
The compression ratio (\(r\)) is defined as:
\[ r = \frac{V_{\text{total}}}{V_{\text{c}}} = \frac{V_{\text{s}} + V_{\text{c}}}{V_{\text{c}}} \]

Step 2: Detailed Explanation:
Let us analyze the definition:
- The maximum volume of the cylinder occurs when the piston is at the bottom of its stroke (Bottom Dead Center, BDC). This is the total cylinder volume (\(V_{\text{total}}\)).
- The minimum volume occurs when the piston is at the top of its stroke (Top Dead Center, TDC). This is the clearance volume (\(V_{\text{c}}\)).
- Therefore, the compression ratio is the ratio of the total cylinder volume to the clearance volume:
\[ \text{Compression Ratio} = \frac{\text{Total Volume}}{\text{Clearance Volume}} \]

Step 3: Final Answer:
The compression ratio is defined as the ratio of the total volume to the clearance volume. Hence, the correct option is (B).