Total Work done per cycle in Compressor during Incomplete Intercooling given Volume 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%
✖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%
✖Suction volume is the volume of refrigerant sucked by the compressor during its suction stroke.ⓘ Suction volume [V₁]			+10% -10%
✖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.ⓘ Discharge Pressure of Low Pressure Compressor [P₂]			+10% -10%
✖Discharge volume is the volume of the refrigerant after compression or at the discharge.ⓘ Discharge Volume [V₂]			+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%

✖Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source.ⓘ Total Work done per cycle in Compressor during Incomplete Intercooling given Volume [w]

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

Formula

`"w" = ("n"_{"c"}/("n"_{"c"}-1))*"P"_{"1"}*"V"_{"1"}*(("P"_{"2"}/"P"_{"1"})^(("n"_{"c"}-1)/"n"_{"c"})-1)+("n"_{"c"}/("n"_{"c"}-1))*"P"_{"2"}*"V"_{"2"}*(("P"_{"3"}/"P"_{"2"})^(("n"_{"c"}-1)/"n"_{"c"})-1)`

Example

`"944938.8J"=("1.2"/("1.2"-1))*"0.002Bar"*"10m³"*(("7Bar"/"0.002Bar")^(("1.2"-1)/"1.2")-1)+("1.2"/("1.2"-1))*"7Bar"*"1.6m³"*(("15Bar"/"7Bar")^(("1.2"-1)/"1.2")-1)`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
w = (n_c/(n_c-1))*P₁*V₁*((P₂/P₁)^((n_c-1)/n_c)-1)+(n_c/(n_c-1))*P₂*V₂*((P₃/P₂)^((n_c-1)/n_c)-1)
This formula uses 7 Variables

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.
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.
Suction volume - (Measured in Cubic Meter) - Suction volume is the volume of refrigerant sucked by the compressor during its 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.
Discharge Volume - (Measured in Cubic Meter) - Discharge volume is the volume of the refrigerant after compression or at the discharge.
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
Suction Pressure of Low Pressure Compressor: 0.002 Bar --> 200 Pascal (Check conversion here)
Suction volume: 10 Cubic Meter --> 10 Cubic Meter No Conversion Required
Discharge Pressure of Low Pressure Compressor: 7 Bar --> 700000 Pascal (Check conversion here)
Discharge Volume: 1.6 Cubic Meter --> 1.6 Cubic Meter No Conversion Required
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w = (n_c/(n_c-1))*P₁*V₁*((P₂/P₁)^((n_c-1)/n_c)-1)+(n_c/(n_c-1))*P₂*V₂*((P₃/P₂)^((n_c-1)/n_c)-1) --> (1.2/(1.2-1))*200*10*((700000/200)^((1.2-1)/1.2)-1)+(1.2/(1.2-1))*700000*1.6*((1500000/700000)^((1.2-1)/1.2)-1)

Evaluating ... ...

w = 944938.819325573

STEP 3: Convert Result to Output's Unit

944938.819325573 Joule --> No Conversion Required

FINAL ANSWER

944938.819325573 ≈ 944938.8 Joule <-- Work Done per cycle

(Calculation completed in 00.004 seconds)

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

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< 8 Work Done by Two-Stage Compressor 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

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

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

How does a Two stage reciprocating compressor work?

This type of compressor has two pistons which use for air compression. The piston of the L.P cylinder compresses the air and transfers the pressurized air into the second H.P for further compression where the second piston compresses it. These compressors operate with natural gas or electricity.

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

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume calculator uses 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) to calculate the Work Done per cycle, Total Work done per cycle in Compressor during Incomplete Intercooling given Volume is defined as the amount of total work done per cycle by the two-stage compressor when the intercooling is incomplete. Work Done per cycle is denoted by w symbol.

How to calculate Total Work done per cycle in Compressor during Incomplete Intercooling given Volume using this online calculator? To use this online calculator for Total Work done per cycle in Compressor during Incomplete Intercooling given Volume, enter Polytropic Index for Compression (n_c), Suction Pressure of Low Pressure Compressor (P₁), Suction volume (V₁), Discharge Pressure of Low Pressure Compressor (P₂), Discharge Volume (V₂) & Discharge Pressure of High Pressure Compressor (P₃) and hit the calculate button. Here is how the Total Work done per cycle in Compressor during Incomplete Intercooling given Volume calculation can be explained with given input values -> 944938.8 = (1.2/(1.2-1))*200*10*((700000/200)^((1.2-1)/1.2)-1)+(1.2/(1.2-1))*700000*1.6*((1500000/700000)^((1.2-1)/1.2)-1).

FAQ

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

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume is defined as the amount of total work done per cycle by the two-stage compressor when the intercooling is incomplete and is represented as w = (n_c/(n_c-1))*P₁*V₁*((P₂/P₁)^((n_c-1)/n_c)-1)+(n_c/(n_c-1))*P₂*V₂*((P₃/P₂)^((n_c-1)/n_c)-1) or 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). 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, 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 volume is the volume of refrigerant sucked by the compressor during its 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, Discharge volume is the volume of the refrigerant after compression or at the discharge & 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 Incomplete Intercooling given Volume?

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume is defined as the amount of total work done per cycle by the two-stage compressor when the intercooling is incomplete is calculated using 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). To calculate Total Work done per cycle in Compressor during Incomplete Intercooling given Volume, you need Polytropic Index for Compression (n_c), Suction Pressure of Low Pressure Compressor (P₁), Suction volume (V₁), Discharge Pressure of Low Pressure Compressor (P₂), Discharge Volume (V₂) & Discharge Pressure of High Pressure Compressor (P₃). With our tool, you need to enter the respective value for Polytropic Index for Compression, Suction Pressure of Low Pressure Compressor, Suction volume, Discharge Pressure of Low Pressure Compressor, Discharge Volume & 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, Suction Pressure of Low Pressure Compressor, Suction volume, Discharge Pressure of Low Pressure Compressor, Discharge Volume & 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))*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))*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)
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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