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

STEP 0: Pre-Calculation Summary
Formula Used
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 = (nc/(nc-1))*m*[R]*T1*((P2/P1)^((nc-1)/nc)+(P3/P2)^((nc-1)/nc)-2)
This formula uses 1 Constants, 7 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Work Done per cycle - (Measured in Joule) - Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source.
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 Low Pressure Compressor - (Measured in Pascal) - The Discharge pressure of Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler.
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.
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.
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 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 = (nc/(nc-1))*m*[R]*T1*((P2/P1)^((nc-1)/nc)+(P3/P2)^((nc-1)/nc)-2) --> (1.2/(1.2-1))*0.0333333333333333*[R]*300*((700000/200)^((1.2-1)/1.2)+(1500000/700000)^((1.2-1)/1.2)-2)
Evaluating ... ...
w = 1512.55375434259
STEP 3: Convert Result to Output's Unit
1512.55375434259 Joule --> No Conversion Required
FINAL ANSWER
1512.55375434259 1512.554 Joule <-- Work Done per cycle
(Calculation completed in 00.020 seconds)

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8 Work Done by a Two-Stage Reciprocating Compressor with Intercooler Calculators

Total Work done per cycle in Compressor during incomplete Intercooling given Temperature
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))+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 in Compressor during Incomplete Intercooling given Volume
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)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((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 Complete Intercooling given Suction Volume
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)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature
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)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp
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 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)
Work done per cycle in Low Pressure Compressor during incomplete intercooling given Suction Temp
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 High pressure Compressor during incomplete intercooling given suction volume
Go Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge 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
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

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 = (nc/(nc-1))*m*[R]*T1*((P2/P1)^((nc-1)/nc)+(P3/P2)^((nc-1)/nc)-2)

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 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 Work Done per cycle, The Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume formula is defined as the amount of work done per cycle by the two-stage compressor during the complete intercooling (i.e. discharge pressure of low pressure compressor and suction pressure of high pressure compressor is same) when the suction volume is given. Work Done per cycle is denoted by w 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 (nc), 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 -> 1512.554 = (1.2/(1.2-1))*0.0333333333333333*[R]*300*((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?
The Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume formula is defined as the amount of work done per cycle by the two-stage compressor during the complete intercooling (i.e. discharge pressure of low pressure compressor and suction pressure of high pressure compressor is same) when the suction volume is given and is represented as w = (nc/(nc-1))*m*[R]*T1*((P2/P1)^((nc-1)/nc)+(P3/P2)^((nc-1)/nc)-2) or 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 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 Low pressure compressor is the pressure of the refrigerant at the point where it exits the Low-Pressure compressor. It is also called Pressure at the entry of intercooler, 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 & 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.
How to calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume?
The Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume formula is defined as the amount of work done per cycle by the two-stage compressor during the complete intercooling (i.e. discharge pressure of low pressure compressor and suction pressure of high pressure compressor is same) when the suction volume is given is calculated using 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 (nc), 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 Work Done per cycle?
In this formula, 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 7 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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 = (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)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
  • 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 = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
  • Work Done per cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of refrigerant in kg per minute*[R]*Suction Temperature at 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)
  • 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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