Minimum Work required when Temperature at end of Cooling in Intercooler is fixed 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 at Low Pressure Compressor is the temperature of the refrigerant at the inlet or during the suction stroke.ⓘ Suction temperature at Low pressure Compressor [T₁]			+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 Temperature at end of Cooling in Intercooler is fixed [W]

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Formula

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

Formula

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

Example

`"1100.901J"=2*("1.2"/("1.2"-1))*"2kg/min"*"[R]"*"300K"*(("15Bar"/"0.002Bar")^(("1.2"-1)/(2*"1.2"))-1)`

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Minimum Work required when Temperature at end of Cooling in Intercooler is fixed 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 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)
W = 2*(n_c/(n_c-1))*m*[R]*T₁*((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 at Low pressure Compressor - (Measured in Kelvin) - The Suction temperature at Low Pressure Compressor is the temperature of the refrigerant at the 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 at Low pressure Compressor: 300 Kelvin --> 300 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]*T₁*((P₃/P₁)^((n_c-1)/(2*n_c))-1) --> 2*(1.2/(1.2-1))*0.0333333333333333*[R]*300*((1500000/200)^((1.2-1)/(2*1.2))-1)

Evaluating ... ...

W = 1100.90089454974

STEP 3: Convert Result to Output's Unit

1100.90089454974 Joule --> No Conversion Required

FINAL ANSWER

1100.90089454974 ≈ 1100.901 Joule <-- Work Required

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Minimum Work » Minimum Work required when Temperature at end of Cooling in Intercooler is fixed

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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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< 8 Minimum Work 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 Temperature at end of Cooling in Intercooler is fixed Formula

Advantages of multi-stage compressor over single stage compressor

1. The fluid can be compressed to very high pressure.
2. The intercooler is more efficient than the cylinder wall cooling in a single-stage compressor. For the same pressure, the work done per unit weight of the fluid is low in a compound compressor than that of single-stage compression.
3. Reduce the cost of the compression process.
4. For a given pressure ratio, the multistage arrangement improves volumetric efficiency.
5. The lower temperature range in each stage of compression improves lubrication.
6. Pressure ratio per each stage is lowered and it reduces the leakage loss.
7. The size cylinders of the multi-stage compressors can be adjusted to suit the compression requirement.

How to Calculate Minimum Work required when Temperature at end of Cooling in Intercooler is fixed?

Minimum Work required when Temperature at end of Cooling in Intercooler is fixed calculator uses 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) to calculate the Work Required, The Minimum Work required when Temperature at end of Cooling in Intercooler is fixed formula is defined as the minimum amount of work required to run the multi stage compressor when the temperature at the end of cooling in the intercooler is fixed/constant. Work Required is denoted by W symbol.

How to calculate Minimum Work required when Temperature at end of Cooling in Intercooler is fixed using this online calculator? To use this online calculator for Minimum Work required when Temperature at end of Cooling in Intercooler is fixed, enter Polytropic Index for Compression (n_c), Mass of refrigerant in kg per minute (m), Suction temperature at Low pressure Compressor (T₁), 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 Temperature at end of Cooling in Intercooler is fixed calculation can be explained with given input values -> 1100.901 = 2*(1.2/(1.2-1))*0.0333333333333333*[R]*300*((1500000/200)^((1.2-1)/(2*1.2))-1).

FAQ

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

The Minimum Work required when Temperature at end of Cooling in Intercooler is fixed formula is defined as the minimum amount of work required to run the multi stage compressor when the temperature at the end of cooling in the intercooler is fixed/constant and is represented as W = 2*(n_c/(n_c-1))*m*[R]*T₁*((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 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). 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 at Low Pressure Compressor is the temperature of the refrigerant at the 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 Temperature at end of Cooling in Intercooler is fixed?

The Minimum Work required when Temperature at end of Cooling in Intercooler is fixed formula is defined as the minimum amount of work required to run the multi stage compressor when the temperature at the end of cooling in the intercooler is fixed/constant 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 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). To calculate Minimum Work required when Temperature at end of Cooling in Intercooler is fixed, you need Polytropic Index for Compression (n_c), Mass of refrigerant in kg per minute (m), Suction temperature at Low pressure Compressor (T₁), 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 at Low pressure Compressor, 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 at Low pressure Compressor, 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 = (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))
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)

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