Work Done During Isothermal Compression Given Temperature And Pressure Ratio Calculator

Formula Used:

\[ W_{Isothermal} = 2.3 \times m \times [R] \times T_{refrigerant} \times \ln\left(\frac{P_2}{P_1}\right) \]

Mass of refrigerant in kg per minute:

kg/min

Suction Temperature of Refrigerant:

Discharge Pressure of Refrigerant:

Suction pressure:

Work done per minute during Isothermal Compression:

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1. What is the Isothermal Compression Work Formula?

The formula calculates the work done per minute during isothermal compression of refrigerant. It accounts for mass flow rate, temperature, and pressure ratio using the universal gas constant and natural logarithm function.

2. How Does the Calculator Work?

The calculator uses the isothermal compression work formula:

\[ W_{Isothermal} = 2.3 \times m \times [R] \times T_{refrigerant} \times \ln\left(\frac{P_2}{P_1}\right) \]

Where:

\( m \) — Mass of refrigerant in kg per minute
\( [R] \) — Universal gas constant (8.314 J/mol·K)
\( T_{refrigerant} \) — Suction temperature of refrigerant (K)
\( P_2 \) — Discharge pressure of refrigerant (Pa)
\( P_1 \) — Suction pressure (Pa)

Explanation: The formula calculates the work required to compress refrigerant isothermally, considering the pressure ratio and thermodynamic properties.

3. Importance of Isothermal Compression Calculation

Details: Accurate calculation of isothermal compression work is crucial for refrigeration system design, energy efficiency analysis, and compressor sizing in thermodynamic applications.

4. Using the Calculator

Tips: Enter mass flow rate in kg/min, temperature in Kelvin, and both pressures in Pascals. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is isothermal compression?
A: Isothermal compression is a thermodynamic process where gas is compressed at constant temperature, requiring heat removal during compression.

Q2: Why use natural logarithm in the formula?
A: The natural logarithm accounts for the logarithmic relationship between pressure ratio and work done in isothermal processes.

Q3: What are typical pressure ratios in refrigeration?
A: Pressure ratios typically range from 3:1 to 10:1 depending on the refrigerant type and operating conditions.

Q4: How does temperature affect compression work?
A: Higher suction temperatures generally require more work for compression, as work is directly proportional to temperature in this formula.

Q5: Are there limitations to this equation?
A: This equation assumes ideal gas behavior and perfect isothermal conditions, which may not fully represent real-world compressor performance.