Total Work Done Per Cycle In Compressor During Complete Intercooling Given Suction Volume Calculator

Formula Used:

\[ Work\ Done\ per\ cycle = \frac{n_c}{n_c - 1} \times m \times R \times T_1 \times \left( \left( \frac{P_2}{P_1} \right)^{\frac{n_c - 1}{n_c}} + \left( \frac{P_3}{P_2} \right)^{\frac{n_c - 1}{n_c}} - 2 \right) \]

Polytropic Index for Compression (n_c):

Mass of Refrigerant (m):

kg/min

Suction Temperature at Low Pressure Compressor (T_1):

Suction Pressure of Low Pressure Compressor (P_1):

Discharge Pressure of Low Pressure Compressor (P_2):

Discharge Pressure of High Pressure Compressor (P_3):

Work Done Per Cycle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Work Done Per Cycle Formula?

The formula calculates the total work done per cycle in a compressor during complete intercooling. It accounts for the polytropic compression process and intercooling between compression stages.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( n_c \) — Polytropic Index for Compression
\( m \) — Mass of refrigerant (kg/min)
\( R \) — Universal gas constant (8.314 J/mol·K)
\( T_1 \) — Suction temperature at Low Pressure Compressor (K)
\( P_1 \) — Suction Pressure of Low Pressure Compressor (Pa)
\( P_2 \) — Discharge Pressure of Low Pressure Compressor (Pa)
\( P_3 \) — Discharge Pressure of High Pressure Compressor (Pa)

Explanation: The formula calculates work done considering polytropic compression in both stages with complete intercooling.

3. Importance of Work Calculation

Details: Accurate work calculation is crucial for compressor design, energy efficiency analysis, and system performance optimization in refrigeration and air conditioning systems.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure polytropic index is greater than 1, and all pressure/temperature values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is polytropic index?
A: The polytropic index describes the relationship between pressure and volume during compression/expansion processes that are not perfectly isentropic.

Q2: Why is intercooling important?
A: Intercooling reduces the work required for compression by cooling the gas between stages, making the compression process more efficient.

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

Q4: How does this differ from isentropic work?
A: Polytropic work accounts for real-world inefficiencies and heat transfer during compression, while isentropic work assumes adiabatic reversible compression.

Q5: Can this formula be used for single-stage compression?
A: No, this specific formula is designed for two-stage compression with complete intercooling between stages.