Work Done By Reciprocating Compressor Given Volume Before Compression And After Expansion Calculator

Formula Used:

\[ w = \frac{n_c}{n_c - 1} \times P_1 \times (V_1 - V_4) \times \left( \left( \frac{P_2}{P_1} \right)^{\frac{n_c - 1}{n_c}} - 1 \right) \]

Polytropic Index Of Compression (nc):

Suction Pressure (P1):

Total Volume Of Refrigerant In Compressor (V1):

m³

Expanded Clearance Volume (V4):

m³

Discharge Pressure Of Refrigerant (P2):

Work Done Per Cycle (w):

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1. What Is The Work Done By Reciprocating Compressor?

The work done by a reciprocating compressor per cycle is the total amount of energy transferred to the refrigerant during the compression process. It represents the mechanical work input required to compress the refrigerant from suction pressure to discharge pressure.

2. How Does The Calculator Work?

The calculator uses the polytropic compression formula:

\[ w = \frac{n_c}{n_c - 1} \times P_1 \times (V_1 - V_4) \times \left( \left( \frac{P_2}{P_1} \right)^{\frac{n_c - 1}{n_c}} - 1 \right) \]

Where:

\( w \) — Work Done per cycle (J)
\( n_c \) — Polytropic index of compression
\( P_1 \) — Suction Pressure (Pa)
\( V_1 \) — Total Volume of Refrigerant in Compressor (m³)
\( V_4 \) — Expanded clearance volume (m³)
\( P_2 \) — Discharge Pressure of Refrigerant (Pa)

Explanation: This formula accounts for the polytropic compression process where heat transfer occurs during compression, providing a more accurate representation of real compressor operation.

3. Importance Of Work Done Calculation

Details: Calculating work done per cycle is essential for determining compressor efficiency, power requirements, and overall system performance in refrigeration and air conditioning systems.

4. Using The Calculator

Tips: Enter all values in appropriate units. Ensure polytropic index is greater than 1, and all pressure and volume values are positive. The expanded clearance volume should be less than or equal to the total refrigerant volume.

5. Frequently Asked Questions (FAQ)

Q1: What is the polytropic index of compression?
A: The polytropic index is a parameter that defines the relationship between pressure and volume during compression. It indicates how heat is transferred during the compression process.

Q2: How does this differ from isentropic compression?
A: Isentropic compression assumes no heat transfer (adiabatic and reversible), while polytropic compression accounts for heat transfer during the process, making it more realistic.

Q3: What are typical values for the polytropic index?
A: For reciprocating compressors, the polytropic index typically ranges from 1.1 to 1.3, depending on the refrigerant and operating conditions.

Q4: Why is the expanded clearance volume important?
A: The expanded clearance volume represents the volume of refrigerant remaining in the cylinder after expansion, which affects the actual volume of refrigerant that can be compressed.

Q5: Can this formula be used for all types of compressors?
A: This specific formula is designed for reciprocating compressors. Other compressor types (centrifugal, rotary, etc.) may require different formulas based on their operating principles.