Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp Calculator

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✖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 High Pressure Compressor is the temperature of the refrigerant at the inlet or temperature of the refrigerant leaving the intercooler.ⓘ Suction Temperature at High Pressure Compressor [T₂]			+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 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%

✖Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source.ⓘ Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp [w]

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Formula

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Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp

Formula

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

Example

`"90.09121J"=("1.2"/("1.2"-1))*"2kg/min"*"[R]"*"400K"*(("15Bar"/"7Bar")^(("1.2"-1)/"1.2")-1)`

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Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp 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 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)
w = (n_c/(n_c-1))*m*[R]*T₂*((P₃/P₂)^((n_c-1)/n_c)-1)
This formula uses 1 Constants, 6 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 High Pressure Compressor - (Measured in Kelvin) - The Suction Temperature at High Pressure Compressor is the temperature of the refrigerant at the inlet or temperature of the refrigerant leaving the intercooler.
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.
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.

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 High Pressure Compressor: 400 Kelvin --> 400 Kelvin No Conversion Required
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)
Discharge Pressure of Low Pressure Compressor: 7 Bar --> 700000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w = (n_c/(n_c-1))*m*[R]*T₂*((P₃/P₂)^((n_c-1)/n_c)-1) --> (1.2/(1.2-1))*0.0333333333333333*[R]*400*((1500000/700000)^((1.2-1)/1.2)-1)

Evaluating ... ...

w = 90.0912073805105

STEP 3: Convert Result to Output's Unit

90.0912073805105 Joule --> No Conversion Required

FINAL ANSWER

90.0912073805105 ≈ 90.09121 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 » Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp

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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

Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp Formula

Assumptions in Two-Stage Compression with lntercooler.

The following simplifying assumptions are made in case of two stage-compression with intercooler :
1. The effect of clearance is neglected,
2. There is no pressure drop in the intercooler, and
3. The compression in both the low pressure (L.P.) and high pressure (H.P.) cylinder polytropic i.e. PV^n = C.

How to Calculate Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp?

Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp 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 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) to calculate the Work Done per cycle, The Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp formula is defined as the amount of work done per cycle by the High-pressure compressor in Multistage Compressor when the intercooling is incomplete and Suction temperature is given. Work Done per cycle is denoted by w symbol.

How to calculate Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp using this online calculator? To use this online calculator for Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp, enter Polytropic Index for Compression (n_c), Mass of refrigerant in kg per minute (m), Suction Temperature at High Pressure Compressor (T₂), Discharge Pressure of High Pressure Compressor (P₃) & Discharge Pressure of Low Pressure Compressor (P₂) and hit the calculate button. Here is how the Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp calculation can be explained with given input values -> 90.09121 = (1.2/(1.2-1))*0.0333333333333333*[R]*400*((1500000/700000)^((1.2-1)/1.2)-1).

FAQ

What is Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp?

The Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp formula is defined as the amount of work done per cycle by the High-pressure compressor in Multistage Compressor when the intercooling is incomplete and Suction temperature is given and is represented as w = (n_c/(n_c-1))*m*[R]*T₂*((P₃/P₂)^((n_c-1)/n_c)-1) 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 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). 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 High Pressure Compressor is the temperature of the refrigerant at the inlet or temperature of the refrigerant leaving the intercooler, 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 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.

How to calculate Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp?

The Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp formula is defined as the amount of work done per cycle by the High-pressure compressor in Multistage Compressor when the intercooling is incomplete and Suction temperature 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 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). To calculate Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp, you need Polytropic Index for Compression (n_c), Mass of refrigerant in kg per minute (m), Suction Temperature at High Pressure Compressor (T₂), Discharge Pressure of High Pressure Compressor (P₃) & Discharge Pressure of Low Pressure Compressor (P₂). 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 High Pressure Compressor, Discharge Pressure of High Pressure Compressor & Discharge 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 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 High Pressure Compressor, Discharge Pressure of High Pressure Compressor & Discharge Pressure of Low 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 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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