Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Calculator

✖Polytropic Index For Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.ⓘ Polytropic Index For Compression [n_c]			+10% -10%
✖Mass of Refrigerant in kg Per Minute is the mass on or by which the work is done.ⓘ Mass of Refrigerant in kg Per Minute [m]			+10% -10%
✖The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke.ⓘ Suction Temperature of Refrigerant [T_r]			+10% -10%
✖Discharge Pressure of High Pressure Compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure.ⓘ Discharge Pressure of High Pressure Compressor [P₃]			+10% -10%
✖Suction Pressure of Low Pressure Compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure.ⓘ Suction Pressure of Low Pressure Compressor [P₁]			+10% -10%

✖Work required means work that is necessary in order to provide a covered service sought in connection application.ⓘ Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect [W]

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Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Solution

STEP 0: Pre-Calculation Summary

Formula Used

Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1)
W = 2*(n_c/(n_c-1))*m*[R]*T_r*((P₃/P₁)^((n_c-1)/(2*n_c))-1)
This formula uses 1 Constants, 6 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Work Required - (Measured in Joule) - Work required means work that is necessary in order to provide a covered service sought in connection application.
Polytropic Index For Compression - Polytropic Index For Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.
Mass of Refrigerant in kg Per Minute - (Measured in Kilogram per Second) - Mass of Refrigerant in kg Per Minute is the mass on or by which the work is done.
Suction Temperature of Refrigerant - (Measured in Kelvin) - The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke.
Discharge Pressure of High Pressure Compressor - (Measured in Pascal) - Discharge Pressure of High Pressure Compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure.
Suction Pressure of Low Pressure Compressor - (Measured in Pascal) - Suction Pressure of Low Pressure Compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure.

STEP 1: Convert Input(s) to Base Unit

Polytropic Index For Compression: 1.2 --> No Conversion Required
Mass of Refrigerant in kg Per Minute: 0.03036 Kilogram per Minute --> 0.000506 Kilogram per Second (Check conversion here)
Suction Temperature of Refrigerant: 940 Kelvin --> 940 Kelvin No Conversion Required
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)
Suction Pressure of Low Pressure Compressor: 0.00243 Bar --> 243 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W = 2*(n_c/(n_c-1))*m*[R]*T_r*((P₃/P₁)^((n_c-1)/(2*n_c))-1) --> 2*(1.2/(1.2-1))*0.000506*[R]*940*((1500000/243)^((1.2-1)/(2*1.2))-1)

Evaluating ... ...

W = 50.7563853415876

STEP 3: Convert Result to Output's Unit

50.7563853415876 Joule --> No Conversion Required

FINAL ANSWER

50.7563853415876 ≈ 50.75639 Joule <-- Work Required

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Mechanical » Minimum Work » Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect

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Created by Abhishek Dharmendra Bansile

Vishwakarma Institute of Information Technology, Pune (VIIT Pune), Pune

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national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

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< Minimum Work Calculators

Minimum Work required when Cooling Ratio is fixed

LaTeX Go Work Required = (Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*((Suction Temperature at Low Pressure Compressor*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))+Discharge Temperature of Refrigerant*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-Suction Temperature at Low Pressure Compressor-Discharge Temperature at High Pressure Compressor))

Minimum Work required when Temperature at end of Cooling in Intercooler is fixed

LaTeX Go Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature at Low Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1)

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect

LaTeX Go Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1)

Cooling ratio

LaTeX Go Cooling Ratio = (Suction Temperature at High Pressure Compressor-Discharge Temperature at High Pressure Compressor)/(Suction Temperature at High Pressure Compressor-Suction Temperature at Low Pressure Compressor)

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula

LaTeX Go

What is the difference between perfect intercooling and imperfect intercooling?

When the temperature of the air leaving the intercooling is more than the original atmosphere air temperature, then this is known as incomplete or Imperfect Intercooling. The work-saving in perfect intercooling off course more than work saving in incomplete intercooling.

How to Calculate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect calculator uses Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1) to calculate the Work Required, Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum energy required to cool a refrigerant in a perfect intercooling system with a fixed cooling ratio, which is a critical parameter in refrigeration systems. Work Required is denoted by W symbol.

How to calculate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect using this online calculator? To use this online calculator for Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect, enter Polytropic Index For Compression (n_c), Mass of Refrigerant in kg Per Minute (m), Suction Temperature of Refrigerant (T_r), Discharge Pressure of High Pressure Compressor (P₃) & Suction Pressure of Low Pressure Compressor (P₁) and hit the calculate button. Here is how the Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect calculation can be explained with given input values -> 30.13525 = 2*(1.2/(1.2-1))*0.000506*[R]*940*((1500000/243)^((1.2-1)/(2*1.2))-1).

FAQ

What is Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum energy required to cool a refrigerant in a perfect intercooling system with a fixed cooling ratio, which is a critical parameter in refrigeration systems and is represented as W = 2*(n_c/(n_c-1))*m*[R]*T_r*((P₃/P₁)^((n_c-1)/(2*n_c))-1) or Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1). Polytropic Index For Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index, Mass of Refrigerant in kg Per Minute is the mass on or by which the work is done, The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke, Discharge Pressure of High Pressure Compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure & Suction Pressure of Low Pressure Compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure.

How to calculate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum energy required to cool a refrigerant in a perfect intercooling system with a fixed cooling ratio, which is a critical parameter in refrigeration systems is calculated using Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1). To calculate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect, you need Polytropic Index For Compression (n_c), Mass of Refrigerant in kg Per Minute (m), Suction Temperature of Refrigerant (T_r), Discharge Pressure of High Pressure Compressor (P₃) & Suction Pressure of Low Pressure Compressor (P₁). With our tool, you need to enter the respective value for Polytropic Index For Compression, Mass of Refrigerant in kg Per Minute, Suction Temperature of Refrigerant, Discharge Pressure of High Pressure Compressor & Suction Pressure of Low Pressure Compressor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Work Required?

In this formula, Work Required uses Polytropic Index For Compression, Mass of Refrigerant in kg Per Minute, Suction Temperature of Refrigerant, Discharge Pressure of High Pressure Compressor & Suction Pressure of Low Pressure Compressor. We can use 2 other way(s) to calculate the same, which is/are as follows -

Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature at Low Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1)
Work Required = (Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*((Suction Temperature at Low Pressure Compressor*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))+Discharge Temperature of Refrigerant*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-Suction Temperature at Low Pressure Compressor-Discharge Temperature at High Pressure Compressor))

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