Work done by Reciprocating Compressor given Suction Temperature Calculator

✖Polytropic index of compression.ⓘ Polytropic index of 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 of refrigerant is the temperature of refrigerant at inlet or during the suction stroke.ⓘ Suction Temperature of Refrigerant [T_refrigerant]			+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%
✖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%

✖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 Suction Temperature [w]

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Formula

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Work done by Reciprocating Compressor given Suction Temperature

Formula

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

Example

`"256.8531J"=("1.3"/("1.3"-1))*"2kg/min"*"[R]"*"350K"*(("8Bar"/"1.013Bar")^(("1.3"-1)/"1.3")-1)`

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Work done by Reciprocating Compressor given Suction Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
w = (n_c/(n_c-1))*m*[R]*T_refrigerant*((P₂/P₁)^((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 of compression - Polytropic index of compression.
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 of Refrigerant - (Measured in Kelvin) - The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Polytropic index of compression: 1.3 --> No Conversion Required
Mass of refrigerant in kg per minute: 2 Kilogram per Minute --> 0.0333333333333333 Kilogram per Second (Check conversion here)
Suction Temperature of Refrigerant: 350 Kelvin --> 350 Kelvin No Conversion Required
Discharge Pressure of Refrigerant: 8 Bar --> 800000 Pascal (Check conversion here)
Suction pressure: 1.013 Bar --> 101300 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w = (n_c/(n_c-1))*m*[R]*T_refrigerant*((P₂/P₁)^((n_c-1)/n_c)-1) --> (1.3/(1.3-1))*0.0333333333333333*[R]*350*((800000/101300)^((1.3-1)/1.3)-1)

Evaluating ... ...

w = 256.853071890108

STEP 3: Convert Result to Output's Unit

256.853071890108 Joule --> No Conversion Required

FINAL ANSWER

256.853071890108 ≈ 256.8531 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 Reciprocating Compressor with Clearance Volume » Work done by Reciprocating Compressor given Suction Temperature

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Created by Abhishek Dharmendra Bansile

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

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< 4 Work Done by Reciprocating Compressor with Clearance 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))

Work done by Reciprocating Compressor given Suction Temperature Formula

What is the effect of clearance volume on work done in compressor?

The expansion of this trapped air in the clearance volume causes effective loss of stroke due to which the volumetric efficiency of the compressor drops. Therefore, the clearance volume has a significant effect on the efficiency of the compressor.

How to Calculate Work done by Reciprocating Compressor given Suction Temperature?

Work done by Reciprocating Compressor given Suction Temperature calculator uses 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) to calculate the Work Done per cycle, The Work done by Reciprocating Compressor given Suction Temperature 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 Suction Temperature using this online calculator? To use this online calculator for Work done by Reciprocating Compressor given Suction Temperature, enter Polytropic index of compression (n_c), Mass of refrigerant in kg per minute (m), Suction Temperature of Refrigerant (T_refrigerant), Discharge Pressure of Refrigerant (P₂) & Suction pressure (P₁) and hit the calculate button. Here is how the Work done by Reciprocating Compressor given Suction Temperature calculation can be explained with given input values -> 256.8531 = (1.3/(1.3-1))*0.0333333333333333*[R]*350*((800000/101300)^((1.3-1)/1.3)-1).

FAQ

What is Work done by Reciprocating Compressor given Suction Temperature?

The Work done by Reciprocating Compressor given Suction Temperature 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))*m*[R]*T_refrigerant*((P₂/P₁)^((n_c-1)/n_c)-1) or 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). Polytropic index of compression, Mass of refrigerant in kg per minute is the mass on or by which the work is done, The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke, 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 & The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.

How to calculate Work done by Reciprocating Compressor given Suction Temperature?

The Work done by Reciprocating Compressor given Suction Temperature 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))*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). To calculate Work done by Reciprocating Compressor given Suction Temperature, you need Polytropic index of compression (n_c), Mass of refrigerant in kg per minute (m), Suction Temperature of Refrigerant (T_refrigerant), Discharge Pressure of Refrigerant (P₂) & Suction pressure (P₁). With our tool, you need to enter the respective value for Polytropic index of compression, Mass of refrigerant in kg per minute, Suction Temperature of Refrigerant, Discharge Pressure of Refrigerant & Suction pressure 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, Mass of refrigerant in kg per minute, Suction Temperature of Refrigerant, Discharge Pressure of Refrigerant & Suction pressure. 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))*(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 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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