Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume Calculator

✖Polytropic Index for Compression is a measure of the efficiency of a two-stage compressor, indicating the degree of isentropic compression in a real compression process.ⓘ Polytropic Index for Compression [n_c]			+10% -10%
✖Mass of Refrigerant in kg per minute is defined as the quantity of refrigerant flowing through a system per minute, measured in kilograms.ⓘ Mass of Refrigerant in kg per minute [m]			+10% -10%
✖Suction temperature at Low pressure Compressor is the temperature of the refrigerant at the suction side of the low-pressure compressor in a two-stage compression system.ⓘ Suction Temperature at Low Pressure Compressor [T₁]			+10% -10%
✖Discharge Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor stage of a two-stage compressor discharges compressed air or gas.ⓘ Discharge Pressure of Low Pressure Compressor [P₂]			+10% -10%
✖Suction Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor in a two-stage compressor system draws in air or gas.ⓘ Suction Pressure of Low Pressure Compressor [P₁]			+10% -10%
✖Discharge Pressure of High Pressure Compressor is the pressure at which the high-pressure compressor stage of a two-stage compressor discharges compressed air or gas.ⓘ Discharge Pressure of High Pressure Compressor [P₃]			+10% -10%

✖Total Work Done per cycle is the total energy transferred per cycle in a two-stage compressor, which involves compression in two stages with intermediate cooling.ⓘ Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume [w_t]

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Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
w_t = (n_c/(n_c-1))*m*[R]*T₁*((P₂/P₁)^((n_c-1)/n_c)+(P₃/P₂)^((n_c-1)/n_c)-2)
This formula uses 1 Constants, 7 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Total Work Done per Cycle - (Measured in Joule) - Total Work Done per cycle is the total energy transferred per cycle in a two-stage compressor, which involves compression in two stages with intermediate cooling.
Polytropic Index for Compression - Polytropic Index for Compression is a measure of the efficiency of a two-stage compressor, indicating the degree of isentropic compression in a real compression process.
Mass of Refrigerant in kg per minute - (Measured in Kilogram per Second) - Mass of Refrigerant in kg per minute is defined as the quantity of refrigerant flowing through a system per minute, measured in kilograms.
Suction Temperature at Low Pressure Compressor - (Measured in Kelvin) - Suction temperature at Low pressure Compressor is the temperature of the refrigerant at the suction side of the low-pressure compressor in a two-stage compression system.
Discharge Pressure of Low Pressure Compressor - (Measured in Pascal) - Discharge Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor stage of a two-stage compressor discharges compressed air or gas.
Suction Pressure of Low Pressure Compressor - (Measured in Pascal) - Suction Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor in a two-stage compressor system draws in air or gas.
Discharge Pressure of High Pressure Compressor - (Measured in Pascal) - Discharge Pressure of High Pressure Compressor is the pressure at which the high-pressure compressor stage of a two-stage compressor discharges compressed air or gas.

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: 7216 Kelvin --> 7216 Kelvin No Conversion Required
Discharge Pressure of Low Pressure Compressor: 7 Bar --> 700000 Pascal (Check conversion here)
Suction Pressure of Low Pressure Compressor: 0.002 Bar --> 200 Pascal (Check conversion here)
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w_t = (n_c/(n_c-1))*m*[R]*T₁*((P₂/P₁)^((n_c-1)/n_c)+(P₃/P₂)^((n_c-1)/n_c)-2) --> (1.2/(1.2-1))*0.0333333333333333*[R]*7216*((700000/200)^((1.2-1)/1.2)+(1500000/700000)^((1.2-1)/1.2)-2)

Evaluating ... ...

w_t = 36381.959637787

STEP 3: Convert Result to Output's Unit

36381.959637787 Joule --> No Conversion Required

FINAL ANSWER

36381.959637787 ≈ 36381.96 Joule <-- Total Work Done per Cycle

(Calculation completed in 00.020 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Mechanical » Work Done by Two Stage Compressor » Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume

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Created by Abhishek Dharmendra Bansile

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

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< Work Done by Two Stage Compressor Calculators

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume

LaTeX Go Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Total Work done per cycle in Compressor during incomplete Intercooling given Temperature

LaTeX Go Total Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))+Temperature at Exit of Intercooler*(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-Suction Temperature at Low Pressure Compressor-Temperature at Exit of Intercooler)

Work done per cycle in Low Pressure Compressor during incomplete intercooling given Suction Temp

LaTeX Go Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Work done per cycle in Low pressure Compressor during incomplete intercooling given suction volume

LaTeX Go Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume Formula

LaTeX Go

Why do we use intercooler between compressor stages?

In a two or multistage air compressor, an intercooler is always placed between the low pressure (L.P.) and high pressure (H.P.) cylinder. The purpose of an intercooler is to reduce the work input given to the compressor to reach the same pressure as can be reached by a single compressor.

How to Calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume?

Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume calculator uses Total Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2) to calculate the Total Work Done per Cycle, Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume formula is defined as the total energy transferred per cycle in a two-stage compressor with complete intercooling, considering the suction volume and other relevant parameters, to determine the compressor's performance and efficiency. Total Work Done per Cycle is denoted by w_t symbol.

How to calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume using this online calculator? To use this online calculator for Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume, 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 Low Pressure Compressor (P₂), Suction Pressure of Low Pressure Compressor (P₁) & Discharge Pressure of High Pressure Compressor (P₃) and hit the calculate button. Here is how the Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume calculation can be explained with given input values -> 36381.96 = (1.2/(1.2-1))*0.0333333333333333*[R]*7216*((700000/200)^((1.2-1)/1.2)+(1500000/700000)^((1.2-1)/1.2)-2).

FAQ

What is Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume?

Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume formula is defined as the total energy transferred per cycle in a two-stage compressor with complete intercooling, considering the suction volume and other relevant parameters, to determine the compressor's performance and efficiency and is represented as w_t = (n_c/(n_c-1))*m*[R]*T₁*((P₂/P₁)^((n_c-1)/n_c)+(P₃/P₂)^((n_c-1)/n_c)-2) or Total Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2). Polytropic Index for Compression is a measure of the efficiency of a two-stage compressor, indicating the degree of isentropic compression in a real compression process, Mass of Refrigerant in kg per minute is defined as the quantity of refrigerant flowing through a system per minute, measured in kilograms, Suction temperature at Low pressure Compressor is the temperature of the refrigerant at the suction side of the low-pressure compressor in a two-stage compression system, Discharge Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor stage of a two-stage compressor discharges compressed air or gas, Suction Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor in a two-stage compressor system draws in air or gas & Discharge Pressure of High Pressure Compressor is the pressure at which the high-pressure compressor stage of a two-stage compressor discharges compressed air or gas.

How to calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume?

Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume formula is defined as the total energy transferred per cycle in a two-stage compressor with complete intercooling, considering the suction volume and other relevant parameters, to determine the compressor's performance and efficiency is calculated using Total Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2). To calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume, 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 Low Pressure Compressor (P₂), Suction Pressure of Low Pressure Compressor (P₁) & Discharge Pressure of High Pressure Compressor (P₃). 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 Low Pressure Compressor, Suction Pressure of Low Pressure Compressor & Discharge Pressure of 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 Total Work Done per Cycle?

In this formula, Total Work Done per Cycle uses Polytropic Index for Compression, Mass of Refrigerant in kg per minute, Suction Temperature at Low Pressure Compressor, Discharge Pressure of Low Pressure Compressor, Suction Pressure of Low Pressure Compressor & Discharge Pressure of High Pressure Compressor. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Work Done per Cycle = (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 Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))+Temperature at Exit of Intercooler*(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-Suction Temperature at Low Pressure Compressor-Temperature at Exit of Intercooler)
Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)

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