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

Formula Used:

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

Polytropic Index for Compression (n_c):

(dimensionless)

Suction Pressure of Low Pressure Compressor (P_1):

Suction Volume (V_1):

m³

Discharge Pressure of Low Pressure Compressor (P_2):

Work Done Per Cycle (w):

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1. What is the Work Done Per Cycle Formula?

The formula calculates the work done per cycle in a low pressure compressor during incomplete intercooling. It accounts for the polytropic compression process and the pressure-volume relationship in the compressor system.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( w \) — Work done per cycle (J)
\( n_c \) — Polytropic index for compression (dimensionless)
\( P_1 \) — Suction pressure of low pressure compressor (Pa)
\( V_1 \) — Suction volume (m³)
\( P_2 \) — Discharge pressure of low pressure compressor (Pa)

Explanation: The formula calculates the work input required for the polytropic compression process in the low pressure stage of a multi-stage compression system with incomplete intercooling.

3. Importance of Work Done Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Polytropic index must be greater than 1. All pressure and volume values must be positive. Ensure consistent units throughout.

5. Frequently Asked Questions (FAQ)

Q1: What is polytropic index for compression?
A: The polytropic index (n_c) describes the relationship between pressure and volume during compression. For ideal gases, it ranges between 1 (isothermal) and γ (isentropic).

Q2: Why is incomplete intercooling considered?
A: Incomplete intercooling occurs when the refrigerant is not cooled to the initial suction temperature between compression stages, affecting the work calculation.

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 complete intercooling?
A: With complete intercooling, the refrigerant is cooled to the initial suction temperature, resulting in different work calculations and potentially lower work input.

Q5: What factors affect work done per cycle?
A: Pressure ratio, polytropic index, suction volume, and the degree of intercooling all significantly impact the work required per compression cycle.