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_refrigerant]			+10% -10%
✖The 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%
✖The 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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Formula

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

Formula

`"W" = 2*("n"_{"c"}/("n"_{"c"}-1))*"m"*"[R]"*"T"_{"refrigerant"}*(("P"_{"3"}/"P"_{"1"})^(("n"_{"c"}-1)/(2*"n"_{"c"}))-1)`

Example

`"1284.384J"=2*("1.2"/("1.2"-1))*"2kg/min"*"[R]"*"350K"*(("15Bar"/"0.002Bar")^(("1.2"-1)/(2*"1.2"))-1)`

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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_refrigerant*((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) - The 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) - The 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: 2 Kilogram per Minute --> 0.0333333333333333 Kilogram per Second (Check conversion here)
Suction Temperature of Refrigerant: 350 Kelvin --> 350 Kelvin No Conversion Required
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)
Suction Pressure of Low Pressure Compressor: 0.002 Bar --> 200 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W = 2*(n_c/(n_c-1))*m*[R]*T_refrigerant*((P₃/P₁)^((n_c-1)/(2*n_c))-1) --> 2*(1.2/(1.2-1))*0.0333333333333333*[R]*350*((1500000/200)^((1.2-1)/(2*1.2))-1)

Evaluating ... ...

W = 1284.38437697469

STEP 3: Convert Result to Output's Unit

1284.38437697469 Joule --> No Conversion Required

FINAL ANSWER

1284.38437697469 ≈ 1284.384 Joule <-- Work Required

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Minimum Work Required for a Two-Stage Reciprocating Compressor » 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

Abhishek Dharmendra Bansile has created this Calculator and 100+ more calculators!

Verified by sanjay shiva

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

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< 8 Minimum Work Required for a Two-Stage Reciprocating Compressor Calculators

Minimum Work required when Cooling Ratio is fixed

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

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

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)

Suction Temperature at Low pressure compressor when Cooling ratio is constant

Go Suction temperature at Low pressure Compressor = Discharge Temperature at high pressure compressor/(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))

Discharge Temperature at High pressure compressor when Cooling ratio is constant

Go Discharge Temperature at high pressure compressor = Suction Pressure of Low Pressure Compressor*(Cooling ratio+(1-Cooling ratio)*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))

Suction Temperature at Low Pressure Compressor given Cooling Ratio

Go Suction temperature at Low pressure Compressor = ((Suction Temperature at High Pressure Compressor*Cooling ratio)-Suction Temperature at High Pressure Compressor+Discharge Temperature at high pressure compressor)/Cooling ratio

Cooling ratio

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)

Discharge Temperature at High Pressure Compressor given Cooling Ratio

Go Discharge Temperature at high pressure compressor = Suction Temperature at High Pressure Compressor-Cooling ratio*(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

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, The Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum amount of work required to run the multi-stage compressor when the cooling ratio is fixed and the intercooling is perfect (i.e. the discharge pressure of low-pressure compressor and suction pressure of the high-pressure compressor is same). 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_refrigerant), 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 -> 1284.384 = 2*(1.2/(1.2-1))*0.0333333333333333*[R]*350*((1500000/200)^((1.2-1)/(2*1.2))-1).

FAQ

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

The Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum amount of work required to run the multi-stage compressor when the cooling ratio is fixed and the intercooling is perfect (i.e. the discharge pressure of low-pressure compressor and suction pressure of the high-pressure compressor is same) and is represented as W = 2*(n_c/(n_c-1))*m*[R]*T_refrigerant*((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, The 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 & The 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?

The Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum amount of work required to run the multi-stage compressor when the cooling ratio is fixed and the intercooling is perfect (i.e. the discharge pressure of low-pressure compressor and suction pressure of the high-pressure compressor is same) 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_refrigerant), 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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