Work Done given Polytropic Index for Compression and Expansion Calculator

✖Polytropic index of compression is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during 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%
✖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%
✖Polytropic Index of Expansion is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during expansion.ⓘ Polytropic Index of Expansion [n_e]			+10% -10%
✖Expanded clearance volume is the volume of refrigerant in compressor after expansion.ⓘ Expanded Clearance Volume [V₄]			+10% -10%

✖Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source.ⓘ Work Done given Polytropic Index for Compression and Expansion [w]

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Work Done given Polytropic Index for Compression and 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*((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)
w = (n_c/(n_c-1))*P₁*V₁*((P₂/P₁)^((n_c-1)/n_c)-1)-(n_e/(n_e-1))*P₁*V₄*((P₂/P₁)^((n_e-1)/n_e)-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 of Compression - Polytropic index of compression is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during 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.
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.
Polytropic Index of Expansion - Polytropic Index of Expansion is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during expansion.
Expanded Clearance Volume - (Measured in Cubic Meter) - Expanded clearance volume is the volume of refrigerant in compressor after expansion.

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
Discharge Pressure of Refrigerant: 8 Bar --> 800000 Pascal (Check conversion here)
Polytropic Index of Expansion: 1.2 --> No Conversion Required
Expanded Clearance Volume: 0.6 Cubic Meter --> 0.6 Cubic Meter No Conversion Required

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_e/(n_e-1))*P₁*V₄*((P₂/P₁)^((n_e-1)/n_e)-1) --> (1.3/(1.3-1))*101300*3.36*((800000/101300)^((1.3-1)/1.3)-1)-(1.2/(1.2-1))*101300*0.6*((800000/101300)^((1.2-1)/1.2)-1)

Evaluating ... ...

w = 751318.642818291

STEP 3: Convert Result to Output's Unit

751318.642818291 Joule --> No Conversion Required

FINAL ANSWER

751318.642818291 ≈ 751318.6 Joule <-- Work Done Per Cycle

(Calculation completed in 00.020 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Mechanical » Volume » Work Done given Polytropic Index for Compression and Expansion

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< Volume Calculators

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Stroke Volume of Compressor given Volumetric efficiency

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Stroke Volume of Compressor

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

Work Done given Polytropic Index for Compression and Expansion Formula

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What is polytropic expansion?

A polytropic process is a thermodynamic process that obeys the relation: PV^n = C where P is the pressure, V is volume, n is the polytropic index, and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer.

How to Calculate Work Done given Polytropic Index for Compression and Expansion?

Work Done given Polytropic Index for Compression and Expansion calculator uses 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) to calculate the Work Done Per Cycle, Work Done given Polytropic Index for Compression and Expansion formula is defined as the total energy transferred during a polytropic process, which involves compression and expansion of a gas, and is a critical concept in thermodynamics, particularly in the study of heat engines and refrigeration systems. Work Done Per Cycle is denoted by w symbol.

How to calculate Work Done given Polytropic Index for Compression and Expansion using this online calculator? To use this online calculator for Work Done given Polytropic Index for Compression and Expansion, enter Polytropic index of Compression (n_c), Suction Pressure (P₁), Total Volume of Refrigerant in Compressor (V₁), Discharge Pressure of Refrigerant (P₂), Polytropic Index of Expansion (n_e) & Expanded Clearance Volume (V₄) and hit the calculate button. Here is how the Work Done given Polytropic Index for Compression and Expansion calculation can be explained with given input values -> -181278.40768 = (1.3/(1.3-1))*101300*3.36*((800000/101300)^((1.3-1)/1.3)-1)-(1.2/(1.2-1))*101300*0.6*((800000/101300)^((1.2-1)/1.2)-1).

FAQ

What is Work Done given Polytropic Index for Compression and Expansion?

Work Done given Polytropic Index for Compression and Expansion formula is defined as the total energy transferred during a polytropic process, which involves compression and expansion of a gas, and is a critical concept in thermodynamics, particularly in the study of heat engines and refrigeration systems and is represented as w = (n_c/(n_c-1))*P₁*V₁*((P₂/P₁)^((n_c-1)/n_c)-1)-(n_e/(n_e-1))*P₁*V₄*((P₂/P₁)^((n_e-1)/n_e)-1) or 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). Polytropic index of compression is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during 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, 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, Polytropic Index of Expansion is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during expansion & Expanded clearance volume is the volume of refrigerant in compressor after expansion.

How to calculate Work Done given Polytropic Index for Compression and Expansion?

Work Done given Polytropic Index for Compression and Expansion formula is defined as the total energy transferred during a polytropic process, which involves compression and expansion of a gas, and is a critical concept in thermodynamics, particularly in the study of heat engines and refrigeration systems is calculated using 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). To calculate Work Done given Polytropic Index for Compression and Expansion, you need Polytropic index of Compression (n_c), Suction Pressure (P₁), Total Volume of Refrigerant in Compressor (V₁), Discharge Pressure of Refrigerant (P₂), Polytropic Index of Expansion (n_e) & Expanded Clearance Volume (V₄). With our tool, you need to enter the respective value for Polytropic index of Compression, Suction Pressure, Total Volume of Refrigerant in Compressor, Discharge Pressure of Refrigerant, Polytropic Index of Expansion & Expanded Clearance Volume 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, Discharge Pressure of Refrigerant, Polytropic Index of Expansion & Expanded Clearance Volume. 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))*Mass of Refrigerant Mass Flow Rate*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of Refrigerant/Suction Pressure)^((Polytropic index of Compression-1)/Polytropic index of Compression)-1)

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