Minimum Work required when Cooling Ratio 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%
✖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%
✖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%
✖Discharge Temperature of Refrigerant is the temperature of refrigerant at the outlet or during the discharge stroke.ⓘ Discharge Temperature of Refrigerant [T_d]			+10% -10%
✖Discharge Temperature at High Pressure Compressor is the temperature at which refrigerant leaves the compressor.ⓘ Discharge Temperature at High Pressure Compressor [T₃]			+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 [W]

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Minimum Work required when Cooling Ratio is fixed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
W = (n_c/(n_c-1))*m*[R]*((T₁*(P₃/P₁)^((n_c-1)/(2*n_c))+T_d*(P₃/P₁)^((n_c-1)/(2*n_c))-T₁-T₃))
This formula uses 1 Constants, 8 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) - 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) - 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.
Discharge Temperature of Refrigerant - (Measured in Kelvin) - Discharge Temperature of Refrigerant is the temperature of refrigerant at the outlet or during the discharge stroke.
Discharge Temperature at High Pressure Compressor - (Measured in Kelvin) - Discharge Temperature at High Pressure Compressor is the temperature at which refrigerant leaves the compressor.

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 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: 0.00243 Bar --> 243 Pascal (Check conversion here)
Discharge Temperature of Refrigerant: 970 Kelvin --> 970 Kelvin No Conversion Required
Discharge Temperature at High Pressure Compressor: 310 Kelvin --> 310 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W = (n_c/(n_c-1))*m*[R]*((T₁*(P₃/P₁)^((n_c-1)/(2*n_c))+T_d*(P₃/P₁)^((n_c-1)/(2*n_c))-T₁-T₃)) --> (1.2/(1.2-1))*0.000506*[R]*((300*(1500000/243)^((1.2-1)/(2*1.2))+970*(1500000/243)^((1.2-1)/(2*1.2))-300-310))

Evaluating ... ...

W = 50.9477457986318

STEP 3: Convert Result to Output's Unit

50.9477457986318 Joule --> No Conversion Required

FINAL ANSWER

50.9477457986318 ≈ 50.94775 Joule <-- Work Required

(Calculation completed in 00.020 seconds)

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

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Created by Abhishek Dharmendra Bansile

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

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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 Formula

LaTeX Go

What is Cooling ratio?

The cooling ratio is defined as the ratio of heat abstracted by the cooling system to the heat abstracted to bring the refrigerant to the initial temperature.

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

Minimum Work required when Cooling Ratio is fixed calculator uses 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)) to calculate the Work Required, Minimum Work required when Cooling Ratio is fixed formula is defined as the minimum energy required to cool a system when the cooling ratio is fixed, which is essential in various industrial and engineering applications where efficient cooling systems are crucial. Work Required is denoted by W symbol.

How to calculate Minimum Work required when Cooling Ratio is fixed using this online calculator? To use this online calculator for Minimum Work required when Cooling Ratio 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), Discharge Temperature of Refrigerant (T_d) & Discharge Temperature at High Pressure Compressor (T₃) and hit the calculate button. Here is how the Minimum Work required when Cooling Ratio is fixed calculation can be explained with given input values -> 23.78254 = (1.2/(1.2-1))*0.000506*[R]*((300*(1500000/243)^((1.2-1)/(2*1.2))+970*(1500000/243)^((1.2-1)/(2*1.2))-300-310)).

FAQ

What is Minimum Work required when Cooling Ratio is fixed?

Minimum Work required when Cooling Ratio is fixed formula is defined as the minimum energy required to cool a system when the cooling ratio is fixed, which is essential in various industrial and engineering applications where efficient cooling systems are crucial and is represented as W = (n_c/(n_c-1))*m*[R]*((T₁*(P₃/P₁)^((n_c-1)/(2*n_c))+T_d*(P₃/P₁)^((n_c-1)/(2*n_c))-T₁-T₃)) or 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)). 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, 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 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, Discharge Temperature of Refrigerant is the temperature of refrigerant at the outlet or during the discharge stroke & Discharge Temperature at High Pressure Compressor is the temperature at which refrigerant leaves the compressor.

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

Minimum Work required when Cooling Ratio is fixed formula is defined as the minimum energy required to cool a system when the cooling ratio is fixed, which is essential in various industrial and engineering applications where efficient cooling systems are crucial is calculated using 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)). To calculate Minimum Work required when Cooling Ratio 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), Discharge Temperature of Refrigerant (T_d) & Discharge Temperature at High Pressure Compressor (T₃). 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, Discharge Temperature of Refrigerant & Discharge Temperature at High 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, Discharge Temperature of Refrigerant & Discharge Temperature at High 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 = 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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