Work Done Per Cycle In High Pressure Compressor During Incomplete Intercooling Given Suction Temp Calculator

Formula Used:

\[ Work\ Done\ per\ cycle = \frac{n_c}{n_c - 1} \times m \times [R] \times T_2 \times \left( \left( \frac{P_3}{P_2} \right)^{\frac{n_c - 1}{n_c}} - 1 \right) \]

Polytropic Index for Compression (n_c):

Mass of refrigerant (m):

kg/min

Suction Temperature at High Pressure Compressor (T_2):

Discharge Pressure of High Pressure Compressor (P_3):

Discharge Pressure of Low Pressure Compressor (P_2):

Work Done per cycle:

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1. What is Work Done Per Cycle In High Pressure Compressor?

The work done per cycle in a high pressure compressor during incomplete intercooling represents the mechanical energy required to compress the refrigerant in the high pressure stage of a multi-stage compression system where intercooling is not complete.

2. How Does the Calculator Work?

The calculator uses the polytropic compression formula:

\[ Work\ Done\ per\ cycle = \frac{n_c}{n_c - 1} \times m \times [R] \times T_2 \times \left( \left( \frac{P_3}{P_2} \right)^{\frac{n_c - 1}{n_c}} - 1 \right) \]

Where:

\( n_c \) — Polytropic Index for Compression
\( m \) — Mass flow rate of refrigerant (kg/s)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_2 \) — Suction temperature at high pressure compressor (K)
\( P_3 \) — Discharge pressure of high pressure compressor (Pa)
\( P_2 \) — Discharge pressure of low pressure compressor (Pa)

Explanation: This formula accounts for the polytropic compression process in the high pressure stage, considering the incomplete intercooling condition.

3. Importance of Work Calculation

Details: Accurate calculation of work done is crucial for determining compressor power requirements, system efficiency analysis, and proper sizing of compression equipment in refrigeration and air conditioning systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure polytropic index is greater than 1, all pressure and temperature values are positive, and high pressure discharge pressure is greater than low pressure discharge pressure.

5. Frequently Asked Questions (FAQ)

Q1: What is polytropic compression?
A: Polytropic compression is a process where pressure and volume follow the relationship PV^n = constant, where n is the polytropic index.

Q2: Why is intercooling important in multi-stage compression?
A: Intercooling reduces the work required for compression by cooling the refrigerant between stages, approaching isothermal compression.

Q3: What does incomplete intercooling mean?
A: Incomplete intercooling occurs when the refrigerant is not cooled to the initial suction temperature between compression stages.

Q4: How does polytropic index affect work calculation?
A: The polytropic index determines the nature of compression process - higher values indicate more work required for the same pressure ratio.

Q5: 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.