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

Formula Used:

\[ W = \frac{n_c}{n_c - 1} \times m \times [R] \times T_1 \times \left( \left( \frac{P_2}{P_1} \right)^{\frac{n_c - 1}{n_c}} - 1 \right) \]

Polytropic Index for Compression (nc):

Mass of refrigerant (m):

kg/min

Suction temperature (T₁):

Discharge pressure (P₂):

Suction pressure (P₁):

Work Done per cycle (W):

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

The work done per cycle in a low pressure compressor during incomplete intercooling represents the mechanical energy required to compress the refrigerant in the low 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:

\[ W = \frac{n_c}{n_c - 1} \times m \times [R] \times T_1 \times \left( \left( \frac{P_2}{P_1} \right)^{\frac{n_c - 1}{n_c}} - 1 \right) \]

Where:

\( W \) — Work done per cycle (J)
\( n_c \) — Polytropic index for compression
\( m \) — Mass flow rate of refrigerant (kg/s)
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_1 \) — Suction temperature at low pressure compressor (K)
\( P_2 \) — Discharge pressure of low pressure compressor (Pa)
\( P_1 \) — Suction pressure of low pressure compressor (Pa)

Explanation: This formula accounts for the polytropic compression process where heat transfer occurs during compression, making it more realistic than isentropic assumptions for many practical applications.

3. Importance of Work Calculation

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

4. Using the Calculator

Tips: Enter the polytropic index (typically between 1.1-1.4 for refrigeration compressors), mass flow rate in kg/min, suction temperature in Kelvin, and both suction and discharge pressures in Pascals. All values must be positive with nc > 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the polytropic index (nc)?
A: The polytropic index represents the nature of the compression process. It accounts for both heat transfer and irreversibilities during compression, typically ranging from 1.1 to 1.4 for refrigeration compressors.

Q2: How does incomplete intercooling affect the work?
A: Incomplete intercooling means the refrigerant isn't cooled to the initial suction temperature between stages, resulting in higher suction temperature for subsequent stages and increased work requirement.

Q3: What are typical values for discharge and suction pressures?
A: Suction pressure typically ranges from 100-500 kPa for low-pressure applications, while discharge pressure can range from 500-2000 kPa depending on the system design and refrigerant type.

Q4: How accurate is this calculation compared to real systems?
A: This provides a good theoretical estimate, but actual work may vary due to mechanical losses, valve losses, and other real-world factors not accounted for in the ideal formula.

Q5: Can this formula be used for other gases besides refrigerants?
A: Yes, the formula is general and can be applied to any ideal gas, though the polytropic index may vary depending on the specific gas and compression conditions.