Work Done by Reciprocating Compressor given Volume before Compression and after Expansion Calculator

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Work Done by Reciprocating Compressor with Clearance Volume

Work Done by Single-Stage Compressor

Work Done by Two-Stage Compressor

✖Polytropic index of compression.ⓘ Polytropic index of compression [n_c]			+10% -10%
✖The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.ⓘ Suction pressure [P₁]			+10% -10%
✖Total Volume of Refrigerant in Compressor is the volume of refrigerant in compressor before compression.ⓘ Total Volume of Refrigerant in Compressor [V₁]			+10% -10%
✖Expanded clearance volume is the volume of refrigerant in compressor after expansion.ⓘ Expanded clearance volume [V₄]			+10% -10%
✖The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.ⓘ Discharge Pressure of Refrigerant [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 by Reciprocating Compressor given Volume before Compression and after Expansion [w]

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Formula

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Work Done by Reciprocating Compressor given Volume before Compression and after Expansion

Formula

`"w" = ("n"_{"c"}/("n"_{"c"}-1))*("P"_{"1"}*("V"_{"1"}-"V"_{"4"}))*(("P"_{"2"}/"P"_{"1"})^(("n"_{"c"}-1)/"n"_{"c"})-1)`

Example

`"740324.8J"=("1.3"/("1.3"-1))*("1.013Bar"*("3.36m³"-"0.6m³"))*(("8Bar"/"1.013Bar")^(("1.3"-1)/"1.3")-1)`

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Work Done by Reciprocating Compressor given Volume before Compression and after Expansion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*(Suction pressure*(Total Volume of Refrigerant in Compressor-Expanded clearance volume))*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1)
w = (n_c/(n_c-1))*(P₁*(V₁-V₄))*((P₂/P₁)^((n_c-1)/n_c)-1)
This formula uses 6 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 of compression - Polytropic index of compression.
Suction pressure - (Measured in Pascal) - The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.
Total Volume of Refrigerant in Compressor - (Measured in Cubic Meter) - Total Volume of Refrigerant in Compressor is the volume of refrigerant in compressor before compression.
Expanded clearance volume - (Measured in Cubic Meter) - Expanded clearance volume is the volume of refrigerant in compressor after expansion.
Discharge Pressure of Refrigerant - (Measured in Pascal) - The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.

STEP 1: Convert Input(s) to Base Unit

Polytropic index of compression: 1.3 --> No Conversion Required
Suction pressure: 1.013 Bar --> 101300 Pascal (Check conversion here)
Total Volume of Refrigerant in Compressor: 3.36 Cubic Meter --> 3.36 Cubic Meter No Conversion Required
Expanded clearance volume: 0.6 Cubic Meter --> 0.6 Cubic Meter No Conversion Required
Discharge Pressure of Refrigerant: 8 Bar --> 800000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w = (n_c/(n_c-1))*(P₁*(V₁-V₄))*((P₂/P₁)^((n_c-1)/n_c)-1) --> (1.3/(1.3-1))*(101300*(3.36-0.6))*((800000/101300)^((1.3-1)/1.3)-1)

Evaluating ... ...

w = 740324.832197332

STEP 3: Convert Result to Output's Unit

740324.832197332 Joule --> No Conversion Required

FINAL ANSWER

740324.832197332 ≈ 740324.8 Joule <-- Work Done per cycle

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Volume » Work Done by Reciprocating Compressor given Volume before Compression and after Expansion

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< 15 Volume Calculators

Work Done given Polytropic Index for Compression and Expansion

Go Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*Suction pressure*Total Volume of Refrigerant in Compressor*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1)-(Polytropic index of Expansion/(Polytropic index of Expansion-1))*Suction pressure*Expanded clearance volume*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of Expansion-1)/Polytropic index of Expansion)-1)

Work Done by Reciprocating Compressor given Volume before Compression and after Expansion

Go Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*(Suction pressure*(Total Volume of Refrigerant in Compressor-Expanded clearance volume))*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1)

Work done by Reciprocating Compressor given Suction Temperature

Go Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1)

Suction Temperature given Work done by Compressor

Go Suction Temperature of Refrigerant = (Polytropic index of compression-1)/(Polytropic index of compression*Mass of refrigerant in kg per minute*[R]*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1))

Volumetric Efficiency in Compressor given Clearance Factor

Go Volumetric Efficiency of Compressor = 1+Clearance factor-(Clearance factor*(Discharge Pressure of Refrigerant/Suction pressure)^(1/Polytropic Index for Compression))

Total Volume of Refrigerant in Compressor given Clearance Factor

Go Total Volume of Refrigerant in Compressor = (Clearance volume/Clearance factor)+Clearance volume

Clearance factor

Go Clearance factor = Clearance volume/(Total Volume of Refrigerant in Compressor-Clearance volume)

Total Volume of Refrigerant in Compressor given Actual Volume

Go Total Volume of Refrigerant in Compressor = Actual volume of Refrigerant+Expanded clearance volume

Expanded Clearance Volume given Actual Volume of Compressor

Go Expanded clearance volume = Total Volume of Refrigerant in Compressor-Actual volume of Refrigerant

Actual volume of refrigerant

Go Actual volume of Refrigerant = Total Volume of Refrigerant in Compressor-Expanded clearance volume

Actual Volume of Refrigerant given Volumetric Efficiency

Go Actual volume of Refrigerant = Volumetric Efficiency of Compressor*Stroke Volume of Compressor

Stroke Volume of Compressor given Volumetric efficiency

Go Stroke Volume of Compressor = Actual volume of Refrigerant/Volumetric Efficiency of Compressor

Total Volume of Refrigerant in Compressor given Stroke Volume of Compressor

Go Total Volume of Refrigerant in Compressor = Stroke Volume of Compressor+Clearance volume

Clearance Volume of Compressor given Stroke Volume

Go Clearance volume = Total Volume of Refrigerant in Compressor-Stroke Volume of Compressor

Stroke Volume of Compressor

Go Stroke Volume of Compressor = Total Volume of Refrigerant in Compressor-Clearance volume

Work Done by Reciprocating Compressor given Volume before Compression and after Expansion Formula

What is the clearance volume of a reciprocating compressor?

The clearance volume is the space remaining in the compressor cylinder at the end of the stroke. Clearance is made up of spaces in valve recesses and the space between the piston and cylinder end.

How to Calculate Work Done by Reciprocating Compressor given Volume before Compression and after Expansion?

Work Done by Reciprocating Compressor given Volume before Compression and after Expansion calculator uses Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*(Suction pressure*(Total Volume of Refrigerant in Compressor-Expanded clearance volume))*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1) to calculate the Work Done per cycle, Work Done by Reciprocating Compressor given Volume before Compression and after Expansion formula is defined as the amount of work done by the reciprocating compressor with clearance volume. Work Done per cycle is denoted by w symbol.

How to calculate Work Done by Reciprocating Compressor given Volume before Compression and after Expansion using this online calculator? To use this online calculator for Work Done by Reciprocating Compressor given Volume before Compression and after Expansion, enter Polytropic index of compression (n_c), Suction pressure (P₁), Total Volume of Refrigerant in Compressor (V₁), Expanded clearance volume (V₄) & Discharge Pressure of Refrigerant (P₂) and hit the calculate button. Here is how the Work Done by Reciprocating Compressor given Volume before Compression and after Expansion calculation can be explained with given input values -> 740324.8 = (1.3/(1.3-1))*(101300*(3.36-0.6))*((800000/101300)^((1.3-1)/1.3)-1).

FAQ

What is Work Done by Reciprocating Compressor given Volume before Compression and after Expansion?

Work Done by Reciprocating Compressor given Volume before Compression and after Expansion formula is defined as the amount of work done by the reciprocating compressor with clearance volume and is represented as w = (n_c/(n_c-1))*(P₁*(V₁-V₄))*((P₂/P₁)^((n_c-1)/n_c)-1) or Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*(Suction pressure*(Total Volume of Refrigerant in Compressor-Expanded clearance volume))*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1). Polytropic index of compression, The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant, Total Volume of Refrigerant in Compressor is the volume of refrigerant in compressor before compression, Expanded clearance volume is the volume of refrigerant in compressor after expansion & The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.

How to calculate Work Done by Reciprocating Compressor given Volume before Compression and after Expansion?

Work Done by Reciprocating Compressor given Volume before Compression and after Expansion formula is defined as the amount of work done by the reciprocating compressor with clearance volume is calculated using Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*(Suction pressure*(Total Volume of Refrigerant in Compressor-Expanded clearance volume))*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1). To calculate Work Done by Reciprocating Compressor given Volume before Compression and after Expansion, you need Polytropic index of compression (n_c), Suction pressure (P₁), Total Volume of Refrigerant in Compressor (V₁), Expanded clearance volume (V₄) & Discharge Pressure of Refrigerant (P₂). With our tool, you need to enter the respective value for Polytropic index of compression, Suction pressure, Total Volume of Refrigerant in Compressor, Expanded clearance volume & Discharge Pressure of Refrigerant 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 of compression, Suction pressure, Total Volume of Refrigerant in Compressor, Expanded clearance volume & Discharge Pressure of Refrigerant. We can use 2 other way(s) to calculate the same, which is/are as follows -

Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1)
Work Done per cycle = (Polytropic index of compression/(Polytropic index of compression-1))*Suction pressure*Total Volume of Refrigerant in Compressor*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of compression-1)/Polytropic index of compression)-1)-(Polytropic index of Expansion/(Polytropic index of Expansion-1))*Suction pressure*Expanded clearance volume*((Discharge Pressure of Refrigerant/Suction pressure)^((Polytropic index of Expansion-1)/Polytropic index of Expansion)-1)

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